Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61060 |
| 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 | |
2686 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)(18,26)(19,23)(20,34)(21,24)(22,29)(25,35)(27,42)(28,38)(30,37)(31,45)(32,46)(33,40)(36,44)(39,43)(41,47);(16,18,21,30)(17,22,24,38)(19,31,33,27)(20,28,35,29)(23,39,40,36)(25,37,34,26)(32,44,47,43)(41,42,46,45);(13,15)(16,19,21,33)(17,23,24,40)(18,27,30,31)(20,32,35,47)(22,36,38,39)(25,41,34,46)(26,42,37,45)(28,43,29,44);(18,28)(20,35)(22,37)(25,34)(26,38)(27,43)(29,30)(31,44)(32,47)(36,45)(39,42)(41,46);(17,24)(22,38)(23,40)(25,34)(26,37)(36,39)(41,46)(42,45)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54048);