Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| isoclinism | isoclinic class of D3 |
| automorphism | Aut(G) = D3×#2021 (order 768) · Inn(G) = D3 · Out(G) = #2021 |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C3⋊C8 |
| derived, Sylow | C3 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D3 |
| commutator, hypocenter | C3 | C4×C8 |
| Frattini | C2×C4 | C2×D3 |
| Fitting | C3×C42 | C2 |
| socle, prime radical | C22×C3 | C2×C4 |
| cosocle | C2×C3×C4 | C22 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C42 | |
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)(8,9,10,12,11,13,14,15);(1,2,3)(4,5,6,7)48 conjugacy classes — view the full character table.
| maximal subgroup of | C8×C3⋊C8, #4454, #4455, … |
| maximal normal subgroup of | C8×C3⋊C8, #4454, #4455, … |
| maximal quotient of | C8×C3⋊C8, #4455, C4×C3⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 9);