Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24×C4 |
| direct product | C11×#18465 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#538 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11)(15,22)(17,23)(18,25)(20,26)(28,29,34,39)(30,40,43,53)(31,36,45,51)(32,38,33,37)(35,47,49,42)(41,54,57,58)(44,52,46,50)(48,55,59,56);(12,13)(14,17)(15,18)(16,19)(20,24)(21,23)(22,25)(26,27)(28,30,34,43)(29,35,39,49)(31,41,45,57)(32,42,33,47)(36,48,51,59)(37,40,38,53)(44,55,46,56)(50,58,52,54);(12,14)(13,17)(15,20)(16,21)(18,24)(19,23)(22,26)(25,27)(28,31)(29,36)(30,41)(32,46)(33,44)(34,45)(35,48)(37,52)(38,50)(39,51)(40,54)(42,56)(43,57)(47,55)(49,59)(53,58);(12,15,16,22)(13,18,19,25)(14,20,21,26)(17,24,23,27)(28,32,34,33)(29,37,39,38)(30,42,43,47)(31,44,45,46)(35,40,49,53)(36,50,51,52)(41,55,57,56)(48,58,59,54)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11453);