Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#11413 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×C42 |
| commutator | C2×C4 | C2×C42×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#97 |
| prime radical | C23×C11 | #97 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,17,15,16,18,19)(21,25,26,31)(22,28)(27,34,33,32)(29,35);(20,21,22,27,23,25,29,32,24,26,28,33,30,31,35,34);(13,16)(17,19)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4401);