Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8510 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#8512 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #379 |
| commutator | C42 | C22×C4×C11 |
| Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
652 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,17,19,22)(18,26,27,25)(29,34)(30,37)(31,32)(36,39)(38,40)(41,42);(12,13)(14,18)(15,22)(16,19)(17,24)(20,25)(21,27)(23,26)(28,29)(30,35)(31,39)(32,34)(33,36)(37,42)(38,43)(40,41);(12,14,16,21)(13,18,19,27)(15,23,24,20)(17,25,22,26)(28,30,33,38)(29,35,36,43)(31,37,32,40)(34,41,39,42)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 1500);