Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#11594 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C8 | C22×C8×C11 |
| Frattini, cosocle | C4×C8 | C23×C11 |
| socle | C22×C11 | C2×#102 |
| prime radical | C23×C11 | #102 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,16,15,17,18,19)(20,21)(22,31)(23,28)(24,37)(25,41)(26,30)(27,33)(29,39)(32,45)(34,51)(35,48)(36,46)(38,44)(40,47)(42,49)(43,50);(20,22,26,35)(21,27,30,43)(23,34,25,32)(24,38,40,49)(28,44,41,42)(29,45,46,51)(31,47,48,37)(33,36,50,39);(20,23,26,25)(21,28,30,41)(22,32,35,34)(24,36,40,39)(27,42,43,44)(29,37,46,47)(31,45,48,51)(33,49,50,38)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4582);