Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61086 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#532 ◁ G | |
2666 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17)(18,26)(19,23)(20,34)(21,24)(22,29)(25,37)(27,35)(28,44)(30,42)(31,45)(32,43)(33,40)(36,41)(38,47)(39,46);(16,18,21,30)(17,22,24,27)(19,31,33,47)(20,35,37,29)(23,39,40,44)(25,42,34,26)(28,36,46,32)(38,43,45,41);(13,15)(16,17)(18,27)(19,23)(20,25)(21,24)(22,30)(26,35)(28,45)(29,42)(31,44)(32,41)(33,40)(34,37)(36,43)(38,46)(39,47);(16,19,21,33)(17,23,24,40)(18,28,30,46)(20,36,37,32)(22,38,27,45)(25,43,34,41)(26,44,42,39)(29,47,35,31);(17,24)(22,27)(23,40)(25,34)(26,42)(38,45)(39,44)(41,43)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54074);