Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18365 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
862 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)(14,21)(15,19)(16,25)(17,20)(18,22)(23,27)(24,26)(28,29,33,37)(30,34,40,47)(31,35,42,49)(32,43,44,36)(38,50,52,45)(39,53,54,46)(41,55,56,48)(51,57,59,58);(12,14)(13,18)(15,22)(16,23)(17,24)(19,26)(20,27)(21,25)(28,30)(29,34)(31,38)(32,39)(33,40)(35,45)(36,46)(37,47)(41,51)(42,52)(43,53)(44,54)(48,57)(49,50)(55,58)(56,59);(12,15,17,16)(13,19,20,25)(14,22,24,23)(18,26,27,21)(28,31)(29,35)(30,38)(32,41)(33,42)(34,45)(36,48)(37,49)(39,51)(40,52)(43,55)(44,56)(46,57)(47,50)(53,58)(54,59);(12,15,17,16)(13,19,20,25)(14,23,24,22)(18,21,27,26)(28,32,33,44)(29,36,37,43)(30,39,40,54)(31,41,42,56)(34,46,47,53)(35,48,49,55)(38,51,52,59)(45,57,50,58)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11353);