Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = D3×#120 (order 192) · Inn(G) = (C2×D3)⋊C4 · Out(G) = C22 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #99 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 11 points:
(1,2,3)(4,6)(5,8,9,10)(7,11);(2,3)(4,5)(6,10)(7,9)(8,11)Polycyclic presentation:
2^5,3|b^2=c,b^a=bd,c^a=ce,f^a=f^2,d^b=de21 conjugacy classes — view the full character table.
| maximal subgroup of | #4740, #4741, #4742, … |
| maximal normal subgroup of | #4740, #4741, #4742, … |
| maximal quotient of | #4451, #4452, #4467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 13);