Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = C25×D3 (order 192) · Inn(G) = C2×D3 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊C8 |
| Fitting | C2×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ C22⋊C8 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(5,7)(8,9,10,12,11,13,14,15);(2,3)(4,5)(6,7)Polycyclic presentation:
2^5,3|b^2=c,c^2=e,b^a=bd,f^a=f^236 conjugacy classes — view the full character table.
| maximal subgroup of | #4685, C8×D12, #4688, … |
| maximal normal subgroup of | #4685, C8×D12, #4688, … |
| maximal quotient of | #4456, #4459, #4468, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 27);