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×#11103 |
| 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 | |
836 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)(12,13,17,21,18,22,16,31)(14,23,27,34,26,39,25,19)(15,28,29,36,30,20,32,37)(24,38,40,33,41,43,42,35);(12,14,16,25,18,26,17,27)(13,19,21,23,22,34,31,39)(15,24,29,40,30,41,32,42)(20,35,36,43,28,33,37,38);(12,15)(13,20)(14,24)(16,29)(17,32)(18,30)(19,33)(21,36)(22,28)(23,38)(25,40)(26,41)(27,42)(31,37)(34,35)(39,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4091);