A microscopic framework of sdIBM-2 is extended to the one of sdgIBM-2.
Introducing hexadecupole pairing force, Hamiltonian and E2, E4 operat
ors of the sdgIBM-2 are deduced microscopically. The nucleus Mg-24 in
the light-mass region is chosen as the first application of such an ex
tended microscopic approach. Based on strong coupling picture, spectru
m, reduced E2 transition rates and reduced E4 transition matrix elemen
ts are calculated. The calculated results fit experimental results sui
te well.