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×#33501 |
| 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 | C23×C11 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C11 ◁ G | |
444 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,18)(16,19)(17,22)(21,26)(23,25)(24,27)(28,29,31,36,32,37,41,49,33,35,42,47,43,48,53,57)(30,34,39,45,40,46,52,56,38,44,50,54,51,55,58,59);(12,14,16,22)(13,17,19,20)(15,23,24,21)(18,26,27,25)(28,30)(29,34)(31,39)(32,40)(33,38)(35,44)(36,45)(37,46)(41,52)(42,50)(43,51)(47,54)(48,55)(49,56)(53,58)(57,59);(12,15,16,24)(13,18,19,27)(14,21,22,23)(17,25,20,26)(29,35)(30,38)(36,47)(37,48)(39,50)(40,51)(49,57)(52,58);(13,19)(17,20)(18,27)(25,26)(30,38)(34,44)(39,50)(40,51)(45,54)(46,55)(52,58)(56,59)836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26489);