Finite Group DatabasebetaFinite Group Databasebeta| order | 96 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×#72209833 (order 43008) · Inn(G) = C1 · Out(G) = C2×#72209833 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C26 |
| abelian | C23×C3×C4 |
| multiplicative | (ℤ/280)ˣ, (ℤ/312)ˣ, (ℤ/336)ˣ, (ℤ/360)ˣ, (ℤ/420)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C24×C3 |
| socle, prime radical | C24×C3 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 13 points:
(1,2,3,4)(11,12,13);(5,6);(7,8);(9,10)96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(96, 220);