Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C23×C4 |
| direct product | C11×#33706 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C22×C11×D8 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
598 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
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)(22,34)(23,28)(24,42)(25,45)(26,46)(27,33)(29,36)(30,35)(31,44)(32,43)(37,49)(38,48)(39,47)(40,51)(41,50);(13,16)(17,19)(20,22,35,41,26,38,44,39,27,36,25,37,43,40,24,23)(21,28,42,51,32,49,45,29,33,47,31,48,46,50,30,34);(12,14,15,18)(13,17,16,19)(20,23,24,40,43,37,25,36,27,39,44,38,26,41,35,22)(21,29,30,49,46,51,31,28,33,34,45,50,32,48,42,47);(22,36)(23,39)(28,47)(29,34)(37,41)(38,40)(48,51)(49,50)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26694);