Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#11119 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #394 |
| 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 | |
864 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)(14,24)(15,28,31,20)(16,23)(17,21)(18,22)(19,26)(25,40,42,36)(27,38)(29,43,41,34)(30,37,33,39)(32,35);(12,14,16,26,18,27,17,32)(13,19,21,24,22,35,23,38)(15,29,30,25,31,41,33,42)(20,36,37,34,28,40,39,43);(12,15)(13,20)(14,25)(16,30)(17,33)(18,31)(19,34)(21,37)(22,28)(23,39)(24,40)(26,41)(27,42)(29,32)(35,43)(36,38)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4107);