Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19086 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
854 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)(12,13)(14,20)(15,23)(16,18)(17,22)(19,24)(21,27)(25,26)(28,29,34,39)(30,40,43,50)(31,44,46,52)(32,37,33,38)(35,47,51,42)(36,48,53,45)(41,49,57,59)(54,55,58,56);(15,24)(19,23)(20,27)(22,25)(28,30,34,43)(29,35,39,51)(31,41,46,57)(32,47,33,42)(36,49,53,59)(37,40,38,50)(44,58,52,54)(45,56,48,55);(12,14)(13,17)(15,25)(16,21)(18,26)(19,27)(20,23)(22,24)(28,31)(29,36)(30,41)(32,45)(33,48)(34,46)(35,49)(37,52)(38,44)(39,53)(40,54)(42,55)(43,57)(47,56)(50,58)(51,59);(13,18)(17,26)(19,23)(20,27)(28,32,34,33)(29,37,39,38)(30,42,43,47)(31,45,46,48)(35,50,51,40)(36,52,53,44)(41,55,57,56)(49,58,59,54)341 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 12079);