Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = C2×D3×#120 (order 384) · Inn(G) = D3 · Out(G) = C2×#120 |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic3 |
| derived, Sylow | C3 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D3 |
| commutator, hypocenter | C3 | C4×C8 |
| Frattini | C2×C4 | C2×D3 |
| Fitting | C2×C3×C8 | C2 |
| socle, prime radical | C22×C3 | C2×C4 |
| cosocle | C2×C3×C4 | C22 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 15 points:
(2,3)(4,5,6,7);(1,2,3)(8,9,10,12,11,13,14,15)48 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×C16, Dic3⋊C16, #4502, … |
| maximal normal subgroup of | Dic3×C16, Dic3⋊C16, #4502, … |
| maximal quotient of | C8×C3⋊C8, #4454, Dic3×C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 20);