Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61937 |
| 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 | |
1810 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)(30,39)(31,38)(32,37)(33,36)(34,41)(35,40)(42,43);(12,14,17,24)(13,18,21,22)(15,23,16,25)(19,26,20,27)(28,30)(29,34)(31,42)(32,41)(33,40)(35,38)(36,43)(37,39);(12,15,17,16)(13,19,21,20)(14,23,24,25)(18,26,22,27)(28,30)(29,35)(31,40)(32,41)(33,42)(34,38)(36,39)(37,43);(12,16,17,15)(13,20,21,19)(14,23,24,25)(18,26,22,27);(13,21)(18,22)(19,20)(26,27)(28,31,32,33)(29,36,37,38)(30,40,41,42)(34,35,39,43)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54925);