Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| automorphism | Aut(G) = C22×D3×D4 (order 192) · Inn(G) = C22×D3 · Out(G) = C23 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×M16 |
| Fitting | C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D3 |
| commutator, socle | C2×C3 | C22×C4 |
| Fitting | C3×M16 | C2 |
| prime radical | C22×D3 | C4 |
| cosocle | C3×C4 | C23 |
| hypercenter | M16 | D3 |
| hypocenter | C3 | C2×M16 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ M16 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 11 points:
(2,5)(6,8)(9,10,11);(1,2,3,6,4,5,7,8);(10,11)30 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#100, #4745, D3×#101, … |
| maximal normal subgroup of | D3×#100, #4745, D3×#101, … |
| maximal quotient of | #4701, D3×#97, #4705, … |
| outer automorphism group of | C3×C52⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 113);