Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11247 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11277 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #387 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C2×C11 | #1442 |
| prime radical | C24×C11 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
592 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)(14,22,25,18)(15,26)(16,21)(17,20)(19,28)(23,32,40,38)(24,39,42,33)(27,34,41,43)(29,37)(30,35)(31,36);(12,14)(13,18)(15,27,28,41)(16,24)(17,25)(19,34,26,43)(20,22)(21,33)(23,29,40,30)(31,42)(32,35,38,37)(36,39);(12,15)(13,19,20,26)(14,23)(16,30)(17,28)(18,32,22,38)(21,37,36,35)(24,41)(25,40)(27,42)(29,31)(33,43,39,34)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4265);