Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C22×D3×D4 (order 192) · Inn(G) = D12 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ #104 |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2,3)(5,8,9,10);(2,3)(4,5)(6,8)(7,9)(10,11)Polycyclic presentation:
2^5,3|b^2=c,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #4700, #4717, D3×#104, … |
| maximal normal subgroup of | #4700, #4717, D3×#104, … |
| maximal quotient of | #4451, #4452, #4456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 12);