Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×D42 (order 384) · Inn(G) = (C2×D3)⋊C4 · Out(G) = C23 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #101 |
38 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)(4,6,7,13,8,14,16,19)(5,9,10,17,11,12,15,18);(2,3)(4,5,8,11)(6,12,14,9)(7,15,16,10)(13,17,19,18)Polycyclic presentation:
2^5,3|a^2=e,b^2=c,c^2=e,b^a=bd,c^a=ce,f^a=f^2,d^b=de21 conjugacy classes — view the full character table.
| maximal subgroup of | #4745, #4748, D3×#101, … |
| maximal normal subgroup of | #4745, #4748, D3×#101, … |
| maximal quotient of | #4465, #4469, #4482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 31);