Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33494 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C11 | C24 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C23×C8 |
| prime radical | C11×#532 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
556 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21,23,28,24,29,34,42,25,30,35,43,36,44,47,51)(22,26,32,37,33,38,46,48,31,27,39,40,45,41,49,50);(12,14)(13,16)(15,19)(17,18)(20,22)(21,26)(23,32)(24,33)(25,31)(27,30)(28,37)(29,38)(34,46)(35,39)(36,45)(40,43)(41,44)(42,48)(47,49)(50,51);(14,19)(16,18)(20,22)(21,27)(23,32)(24,33)(25,31)(26,30)(28,40)(29,41)(34,46)(35,39)(36,45)(37,43)(38,44)(42,50)(47,49)(48,51);(13,17)(16,18)(22,31)(26,27)(32,39)(33,45)(37,40)(38,41)(46,49)(48,50)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26482);