Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33393 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#102 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#578 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
1102 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)(12,13,17,22,18,24,38,23)(14,25,28,47,29,52,37,51)(15,20,32,45,30,43,59,46)(16,33,35,21,36,48,64,49)(19,34,40,27,42,56,41,57)(26,50,55,69,53,71,63,72)(31,60,62,44,58,70,75,68)(39,61,66,54,65,74,67,73);(12,14,18,29)(13,19,24,42)(15,26,30,53)(16,34,36,56)(17,37,38,28)(20,39,43,65)(21,47,49,51)(22,41,23,40)(25,33,52,48)(27,35,57,64)(31,61,58,74)(32,63,59,55)(44,69,68,72)(45,67,46,66)(50,60,71,70)(54,62,73,75);(12,15)(13,20)(14,26)(16,31)(17,32)(18,30)(19,39)(21,44)(22,45)(23,46)(24,43)(25,50)(27,54)(28,55)(29,53)(33,60)(34,61)(35,62)(36,58)(37,63)(38,59)(40,66)(41,67)(42,65)(47,69)(48,70)(49,68)(51,72)(52,71)(56,74)(57,73)(64,75);(15,30)(20,43)(26,53)(31,58)(32,59)(39,65)(44,68)(45,46)(50,71)(54,73)(55,63)(60,70)(61,74)(62,75)(66,67)(69,72)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26381);