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) = C22 |
No aliases for this group.
| Fitting | C2×C3×C8 ⋊ C2 |
| Sylow | C3 ⋊ #102 |
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)(4,5,6,7)(8,9,10,12,11,13,14,15);(2,3)(9,12)(10,14)(13,15)Polycyclic presentation:
2^5,3|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 | C4×#204, C4×D24, #4694, … |
| maximal normal subgroup of | C4×#204, C4×D24, #4694, … |
| maximal quotient of | #4459, #4470, #4485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 28);