Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2218 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33701 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C11×#3147 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
590 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,35)(23,28)(24,30)(25,44)(26,46)(27,34)(29,38)(31,42)(32,45)(33,43)(36,48)(37,49)(39,47)(40,51)(41,50);(13,16)(17,19)(20,22,26,37,24,36,25,23,27,38,42,39,43,40,45,41)(21,28,32,48,33,49,31,35,34,50,44,51,30,47,46,29);(12,14,15,18)(13,17,16,19)(20,23,25,40,43,37,26,38,27,41,45,36,24,39,42,22)(21,29,31,49,30,51,32,28,34,35,46,47,33,48,44,50);(20,24,27,43)(21,30,34,33)(22,36,38,40)(23,39,41,37)(25,42,45,26)(28,47,50,49)(29,51,35,48)(31,32,46,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26689);