Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11109 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #390 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1439 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
852 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)(14,23)(15,27,29,37)(16,30)(17,21)(18,22)(19,25)(20,28,38,32)(24,36,42,33)(26,34)(31,35)(39,41,43,40);(12,14,16,25,18,26,17,31)(13,19,21,23,22,35,30,34)(15,24,28,40,29,42,32,41)(20,36,37,43,38,33,27,39);(12,15)(13,20)(14,24)(16,28)(17,32)(18,29)(19,33)(21,37)(22,38)(23,39)(25,40)(26,42)(27,30)(31,41)(34,43)(35,36)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4097);