Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61071 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61078 |
| 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×#525 ◁ G | |
2694 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
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)(16,17,22,26)(18,27,30,37)(19,24,21,34)(20,25,33,42)(23,35,39,28)(29,44,46,41)(31,40,36,43)(32,47,45,38);(16,18)(17,23)(19,28)(20,32)(21,35)(22,30)(24,37)(25,41)(26,39)(27,34)(29,31)(33,45)(36,46)(38,43)(40,47)(42,44);(13,15)(16,19,22,21)(17,24,26,34)(18,28,30,35)(20,31,33,36)(23,37,39,27)(25,40,42,43)(29,45,46,32)(38,41,47,44);(16,20,22,33)(17,25,26,42)(18,29,30,46)(19,31,21,36)(23,38,39,47)(24,40,34,43)(27,44,37,41)(28,45,35,32);(17,26)(18,30)(24,34)(25,42)(28,35)(29,46)(32,45)(40,43)605 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54066);