Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#23834 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#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 ◁ C4×C11 ◁ C22×C8×C11 ◁ G | |
608 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)(25,37,40,42)(28,34)(29,35)(30,41)(32,39,43,38);(14,24,26,27)(15,28)(19,23,33,36)(20,34)(25,39,40,38)(29,30)(32,42,43,37)(35,41);(12,14)(13,19)(15,25)(16,24)(17,27)(18,26)(20,32)(21,36)(22,33)(23,31)(28,40)(29,38)(30,39)(34,43)(35,42)(37,41);(12,15,16,29,18,28,17,30)(13,20,21,35,22,34,31,41)(14,25,24,38,26,40,27,39)(19,32,36,42,33,43,23,37)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16822);