Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of #204 |
| automorphism | Aut(G) = D3×#3003 (order 768) · Inn(G) = D12 · Out(G) = C22×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #106 |
36 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)(8,9,10,12,11,13,14,15);(2,3)(4,5,6,7)(9,12)(10,14)(13,15)Polycyclic presentation:
2^5,3|a^2=c,b^2=d,d^2=e,b^a=bd,d^a=de,f^a=f^230 conjugacy classes — view the full character table.
| maximal subgroup of | #4494, #4513, #4518, … |
| maximal normal subgroup of | #4494, #4513, #4518, … |
| maximal quotient of | #4457, #4513, #4551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 24);