Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | Aut(G) = D3×#144366 (order 3072) · Inn(G) = C2×D3 · Out(G) = #10336 |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#217 |
| Sylow | C3 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3 |
| commutator | C2×C3 | C22×C4 |
| Frattini | C22 | C22×D3 |
| Fitting, prime radical | C24×C3 | C2 |
| socle | C23×C3 | C22 |
| cosocle | C22×C3 | C23 |
| hypercenter | C24 | D3 |
| hypocenter | C3 | C2×C22⋊C4 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ C24 | |
132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 13 points:
(3,4,5)(6,7)(8,9);(4,5)(7,9)(10,11,12,13);(1,2)36 conjugacy classes — view the full character table.
| maximal subgroup of | #4526, #4527, Dic3×C22⋊C4, … |
| maximal normal subgroup of | #4526, #4527, Dic3×C22⋊C4, … |
| maximal quotient of | C2×#830, #5207, C2×C3⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 159);