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×#33465 |
| 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 | C2×C11×#508 | 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)(12,13,17,24,19,22,18,39)(14,25,28,52,29,51,40,49)(15,21,32,46,30,47,33,62)(16,34,36,48,38,64,37,23)(20,35,43,56,42,65,44,27)(26,50,55,71,53,72,63,69)(31,58,60,70,57,74,61,45)(41,59,66,73,68,75,67,54);(12,14)(13,20)(15,26)(16,35)(17,28)(18,40)(19,29)(21,41)(22,42)(23,49)(24,43)(25,34)(27,37)(30,53)(31,59)(32,55)(33,63)(36,56)(38,65)(39,44)(45,69)(46,66)(47,68)(48,52)(50,58)(51,64)(54,61)(57,75)(60,73)(62,67)(70,71)(72,74);(12,15,17,32,19,30,18,33)(13,21,24,46,22,47,39,62)(14,26,28,55,29,53,40,63)(16,31,36,60,38,57,37,61)(20,41,43,66,42,68,44,67)(23,45,34,58,48,70,64,74)(25,50,52,71,51,72,49,69)(27,54,35,59,56,73,65,75);(13,22)(15,30)(20,42)(23,48)(24,39)(25,51)(26,53)(31,57)(32,33)(34,64)(43,44)(49,52)(54,73)(55,63)(59,75)(60,61)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26453);