Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#19150 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| socle | C22×C11 | C2×#121 |
| prime radical | C23×C11 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G | |
586 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,25)(17,20)(18,24)(22,27)(23,26)(28,29,32,35)(30,36,38,43)(31,39,41,34)(33,40,42,37);(12,14,16,24,17,22,15,23)(13,18,19,21,20,26,25,27);(14,22)(18,26)(21,27)(23,24)(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36);(12,15,17,16)(13,19,20,25)(14,23,22,24)(18,21,26,27)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12138);