Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2032 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11280 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #393 |
| commutator | C24 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1442 |
| prime radical | C24×C11 | C22×C4 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
580 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,21,17,20,31,37)(14,22,25,38,24,18,30,33)(15,26,29,40,28,19,34,36)(23,32,39,42,27,35,41,43);(12,14)(13,18)(15,27,28,23)(16,30)(17,24)(19,35,26,32)(20,22)(21,38)(25,31)(29,39,34,41)(33,37)(36,42,40,43);(12,15)(13,19,20,26)(14,23)(16,29)(17,28)(18,32,22,35)(21,36,37,40)(24,27)(25,39)(30,41)(31,34)(33,42,38,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4268);