Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | Aut(G) = C2×#72209832 (order 6144) · Inn(G) = C22 · Out(G) = C2×#87588⋊C2 |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×C3×D4 |
| unambiguous semidirect product | C4⋊(C23×C3) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C3 | C22 |
| commutator, Frattini, cosocle | C2 | C24×C3 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C3 ◁ G | |
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:
(1,2)(5,6,7);(3,4);(1,2)(3,4)(9,11);(1,2)(3,4)(8,9)(10,11)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 221);