Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#22460 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#578 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1286 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)(12,13,18,23,19,24,17,37)(14,25,28,20,29,44,38,43)(15,30,32,46,33,21,40,47)(16,22,35,51,36,50,39,49)(26,54,57,41,58,52,56,61)(27,53,59,42,60,48,34,67)(31,62,65,71,66,45,64,70)(55,69,63,68,73,72,74,75);(12,14)(13,20)(15,26)(16,34)(17,38)(18,28)(19,29)(21,41)(22,48)(23,44)(24,43)(25,37)(27,35)(30,61)(31,63)(32,57)(33,58)(36,59)(39,60)(40,56)(42,49)(45,69)(46,54)(47,52)(50,53)(51,67)(55,64)(62,72)(65,73)(66,74)(68,70)(71,75);(12,15,19,33)(13,21,24,30)(14,26,29,58)(16,31,36,66)(17,32,18,40)(20,41,43,61)(22,45,50,62)(23,46,37,47)(25,52,44,54)(27,55,60,73)(28,56,38,57)(34,63,59,74)(35,64,39,65)(42,68,67,75)(48,69,53,72)(49,70,51,71);(12,16)(13,22)(14,27)(15,31)(17,39)(18,35)(19,36)(20,42)(21,45)(23,51)(24,50)(25,53)(26,55)(28,59)(29,60)(30,62)(32,65)(33,66)(34,38)(37,49)(40,64)(41,68)(43,67)(44,48)(46,71)(47,70)(52,72)(54,69)(56,74)(57,63)(58,73)(61,75)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 15448);