Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61643 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61938 |
| 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×#533 ◁ G | |
1766 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)(14,22)(15,19)(16,20)(17,21)(18,24)(23,27)(25,26)(28,29)(30,33)(31,34)(32,35)(36,39)(37,41)(38,40)(42,43);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30)(29,33)(31,38)(32,37)(34,40)(35,41)(36,42)(39,43);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(29,34)(31,39)(33,40)(35,36)(38,43)(41,42);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27)(29,35)(30,37)(34,36)(38,43);(13,21)(18,22)(19,20)(26,27)(30,37)(33,41)(38,43)(40,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54926);