Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | Aut(G) = C2×#11713200 (order 1536) · Inn(G) = C22 · Out(G) = C2×D4×S4 |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | C22 |
| commutator, Frattini, cosocle | C2 | C24×C3 |
| socle | C22×C3 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ G | |
164 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2)(3,4,5);(7,10)(11,13);(6,7)(8,11)(9,10)(12,13);(1,2)(6,8,9,12)(7,11,10,13)60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 223);