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×#11110 |
| 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)(12,13,17,21,18,23,16,22)(14,24,27,34,28,38,26,19)(15,29,30,20,32,37,31,36)(25,33,40,43,41,35,42,39);(12,14,16,26,18,28,17,27)(13,19,21,24,23,34,22,38)(15,25,30,40,32,41,31,42)(20,35,29,43,36,33,37,39);(12,15)(13,20)(14,25)(16,30)(17,31)(18,32)(19,33)(21,29)(22,37)(23,36)(24,39)(26,40)(27,42)(28,41)(34,35)(38,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4098);