Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23649 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#397 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22,25,35)(15,19)(16,20)(17,21)(18,24,32,29)(23,38,26,37)(27,33)(28,34)(30,36)(31,40,42,39)(41,43);(12,14)(13,18)(15,26)(16,29)(17,25)(19,31)(20,35)(21,32)(22,36)(23,27)(24,30)(28,39)(33,42)(34,38)(37,43)(40,41);(12,15,16,28,17,27,30,41)(13,19,20,34,21,33,36,43)(14,23,24,39,25,26,29,40)(18,31,22,37,32,42,35,38);(15,27)(19,33)(23,26)(28,41)(31,42)(34,43)(37,38)(39,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16637);