Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#62159 |
| 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×#529 ◁ G | |
1712 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,19)(14,20,21,17)(15,23,24,18)(22,25,27,26)(28,29,32,38)(30,39,41,34)(31,36,33,37)(35,42,43,40);(12,14)(13,17)(15,22)(16,21)(18,25)(19,20)(23,26)(24,27)(28,30)(29,34)(31,42)(32,41)(33,40)(35,36)(37,43)(38,39);(28,30)(29,35)(31,40)(32,41)(33,42)(34,36)(37,39)(38,43);(14,21)(17,20)(22,27)(25,26)(28,31,32,33)(29,36,38,37)(30,40,41,42)(34,43,39,35);(12,15,16,24)(13,18,19,23)(14,22,21,27)(17,25,20,26)(28,31,32,33)(29,37,38,36)(30,40,41,42)(34,35,39,43)539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55147);