Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2031 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23833 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | #2398 |
| prime radical | C11×#575 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
616 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)(14,23,26,36)(15,20)(16,21)(17,31)(18,22)(19,27,33,24)(25,37,39,43)(28,34)(29,41)(30,35)(32,40,42,38);(14,24,26,27)(19,23,33,36)(25,38,39,40)(32,37,42,43);(12,14)(13,19)(15,25)(16,24)(17,27)(18,26)(20,32)(21,36)(22,33)(23,31)(28,38)(29,40)(30,39)(34,43)(35,42)(37,41);(12,15,16,28,18,30,17,29)(13,20,21,34,22,35,31,41)(14,25,24,38,26,39,27,40)(19,32,36,43,33,42,23,37)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16821);