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×#18953 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
846 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)(12,13,18,22)(14,23,15,20)(16,21,17,26)(19,25,27,24)(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);(12,14,18,15)(13,19,22,27)(16,24,17,25)(20,26,23,21)(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);(12,15,18,14)(13,20,22,23)(16,24,17,25)(19,26,27,21)(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)(13,21,22,26)(14,24,15,25)(19,20,27,23)(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, 11941);