Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#11147 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C11 | C23 |
| commutator | C23 | C22×C8×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C24×C11 | C22×C4 |
| prime radical | C25×C11 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C11 ◁ G | |
1206 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(21,22)(24,25,26,28,27,29,30,31);(16,17)(18,19)(20,21)(22,23);(13,15)(17,19)(20,22,23,21)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4135);