Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = D3×#144366 (order 3072) · Inn(G) = D3 · Out(G) = #144366 |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic3 |
| unambiguous semidirect product | (C2×C3)⋊C42 |
| derived, Sylow | C3 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D3 |
| commutator, hypocenter | C3 | C2×C42 |
| Frattini | C22 | C22×D3 |
| Fitting | C22×C3×C4 | C2 |
| socle, prime radical | C23×C3 | C22 |
| cosocle | C22×C3 | C23 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2)(4,5)(6,7,8,9);(3,4,5)(10,11,12,13);(1,2)48 conjugacy classes — view the full character table.
| maximal subgroup of | #4532, #4550, #4555, … |
| maximal normal subgroup of | #4532, #4550, #4555, … |
| maximal quotient of | C2×C4×C3⋊C8, C2×#803, C4×#208, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 129);