Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×B(4,𝔽2) (order 384) · Inn(G) = #217 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #99 |
52 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)(5,8)(7,11)(9,10);(2,3)(4,5)(6,10,11,8)(7,9)Polycyclic presentation:
2^5,3|a^2=c,b^a=bd,d^a=de,f^a=f^2,c^b=ce21 conjugacy classes — view the full character table.
| maximal subgroup of | #4473, #4474, #4475, … |
| maximal normal subgroup of | #4473, #4474, #4475, … |
| maximal quotient of | #4525, #4526, #4528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 41);