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×#61057 |
| 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 | |
2696 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)(16,17,22,27)(18,28,31,42)(19,24,34,41)(20,26,21,25)(23,35,38,30)(29,44,46,39)(32,47,45,37)(33,43,36,40);(16,18,22,31)(17,23,27,38)(19,32,34,45)(20,30,21,35)(24,39,41,44)(25,28,26,42)(29,36,46,33)(37,43,47,40);(13,15);(16,19)(17,24)(18,29)(20,33)(21,36)(22,34)(23,37)(25,40)(26,43)(27,41)(28,44)(30,45)(31,46)(32,35)(38,47)(39,42);(16,20,22,21)(17,25,27,26)(18,30,31,35)(19,33,34,36)(23,28,38,42)(24,40,41,43)(29,45,46,32)(37,44,47,39)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54045);