Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C23×D3×D4 (order 384) · Inn(G) = D12 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #103 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,3)(4,6,7,5)(8,9,10,12,11,13,14,15);(2,3)(4,5,7,6)(9,12)(10,14)(13,15)Polycyclic presentation:
2^5,3|a^2=d,b^2=cd,c^2=e,b^a=bc,c^a=ce,f^a=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #4681, C4×#204, #4697, … |
| maximal normal subgroup of | #4681, C4×#204, #4697, … |
| maximal quotient of | #4456, #4467, #4481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 23);