Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18951 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C23×C11 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
790 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)(12,13,18,15)(14,21,24,27)(16,20,17,25)(19,26,22,23)(28,29)(30,34)(31,41)(32,44)(33,36)(35,43)(37,47)(38,54)(39,52)(40,49)(42,53)(45,50)(46,51)(48,56)(55,58)(57,59);(12,14)(13,19)(15,22)(16,23)(17,26)(18,24)(20,27)(21,25)(28,30,33,40)(29,34,36,49)(31,38,42,55)(32,45,47,39)(35,48,51,59)(37,52,44,50)(41,58,53,54)(43,57,46,56);(12,15,18,13)(14,22,24,19)(16,20,17,25)(21,23,27,26)(28,31)(29,35)(30,38)(32,46)(33,42)(34,48)(36,51)(37,53)(39,57)(40,55)(41,44)(43,47)(45,56)(49,59)(50,58)(52,54);(12,16,18,17)(13,20,15,25)(14,23,24,26)(19,27,22,21)(29,36)(34,49)(35,51)(37,44)(41,53)(48,59)(50,52)(54,58)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11939);