Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33464 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C2×C4×D8 |
| prime radical | C11×#3414 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C11×M16 ◁ C11×#405 ◁ G | |
642 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,17,23,19,24,18,39)(14,25,28,51,29,52,40,48)(15,21,32,47,30,45,33,62)(16,34,36,49,38,64,37,22)(20,35,42,56,44,65,43,27)(26,50,55,72,53,71,63,70)(31,58,60,69,57,74,61,46)(41,59,67,73,66,75,68,54);(12,14)(13,20)(15,26)(16,35)(17,28)(18,40)(19,29)(21,41)(22,48)(23,42)(24,44)(25,34)(27,37)(30,53)(31,59)(32,55)(33,63)(36,56)(38,65)(39,43)(45,66)(46,70)(47,67)(49,51)(50,58)(52,64)(54,61)(57,75)(60,73)(62,68)(69,72)(71,74);(12,15,17,32,19,30,18,33)(13,21,23,47,24,45,39,62)(14,26,28,55,29,53,40,63)(16,31,36,60,38,57,37,61)(20,41,42,67,44,66,43,68)(22,46,34,58,49,69,64,74)(25,50,51,72,52,71,48,70)(27,54,35,59,56,73,65,75);(15,30)(21,45)(26,53)(31,57)(32,33)(41,66)(46,69)(47,62)(50,71)(54,73)(55,63)(58,74)(59,75)(60,61)(67,68)(70,72)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26452);