Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23525 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#394 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1332 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)(14,24)(15,29)(16,21)(17,22)(18,23)(19,27)(20,32)(25,36)(26,35)(28,39)(30,34)(31,38)(33,37)(40,42)(41,43);(12,14)(13,19)(15,30)(16,26)(17,27)(18,28)(20,36)(21,24)(22,39)(23,35)(25,33)(29,43)(31,42)(32,41)(34,38)(37,40);(12,15,16,31,18,33,17,32)(13,20,22,37,23,38,21,29)(14,25,27,42,28,30,26,41)(19,34,24,40,35,36,39,43);(12,16,18,17)(13,21,23,22)(14,26,28,27)(15,31,33,32)(19,24,35,39)(20,29,38,37)(25,41,30,42)(34,40,36,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16513);