Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #213 |
| automorphism | Aut(G) = C22×D3×D4 (order 192) · Inn(G) = #67 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×M16 ⋊ 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)(4,6,7,5,8,9,11,10);(2,3)(4,5)(6,11)(7,9)(8,10)Polycyclic presentation:
2^5,3|b^2=c,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^2,d^b=de24 conjugacy classes — view the full character table.
| maximal subgroup of | #4746, #4747, #4752, … |
| maximal normal subgroup of | #4746, #4747, #4752, … |
| maximal quotient of | #4464, #4465, #4467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 32);