Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = C2×D3×AGL(1,ℤ/8) (order 384) · Inn(G) = D12 · Out(G) = C24 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #108 |
30 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6,8,15,9,16,7,14)(5,10,11,13,12,18,17,19);(2,3)(4,5,7,11,9,12,8,17)(6,13,14,18,16,19,15,10)Polycyclic presentation:
2^5,3|a^2=c,b^2=d,c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #4487, #4493, #4506, … |
| maximal normal subgroup of | #4487, #4493, #4506, … |
| maximal quotient of | #4457, #4458, #4552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 26);