Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = D3×#72209641 (order 9216) · Inn(G) = C2×D3 · Out(G) = #11715850 |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#67 |
| Fitting | C24×C3 ⋊ C2 |
| Sylow | C3 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3 |
| commutator, cosocle | C2×C3 | C24 |
| Frattini | C2 | C23×D3 |
| Fitting | C24×C3 | C2 |
| socle | C23×C3 | C22 |
| hypercenter | C24 | D3 |
| hypocenter | C3 | C22×D4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 11 points:
(5,6,7)(9,11);(6,7)(8,9)(10,11);(3,4);(1,2)36 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#806, #4956, #4957, … |
| maximal normal subgroup of | C2×#806, #4956, #4957, … |
| maximal quotient of | C22×Dic3⋊C4, C2×#924, C22×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 219);