Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#62635 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×D8 |
| commutator, Frattini, cosocle | C8 | C25×C11 |
| socle | C2×C11 | C23×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
2038 conjugacy classes of subgroups.
| minimal degree | μ(G) = 75 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 75 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,25)(15,21)(16,22)(17,35)(18,39)(19,24)(20,28)(23,37)(26,50)(27,51)(29,52)(30,45)(31,46)(32,59)(33,62)(34,49)(36,42)(38,64)(40,48)(41,55)(43,65)(44,56)(47,61)(53,71)(54,72)(57,74)(58,69)(60,67)(63,70)(66,73)(68,75);(12,14)(13,20)(15,26)(16,27)(17,36)(18,40)(19,29)(21,41)(22,42)(23,48)(24,44)(25,35)(28,37)(30,53)(31,54)(32,60)(33,63)(34,56)(38,65)(39,43)(45,66)(46,67)(47,70)(49,51)(50,59)(52,64)(55,61)(57,75)(58,73)(62,68)(69,72)(71,74);(12,15)(13,21)(14,26)(16,31)(17,32)(18,33)(19,30)(20,41)(22,46)(23,47)(24,45)(25,50)(27,54)(28,55)(29,53)(34,58)(35,59)(36,60)(37,61)(38,57)(39,62)(40,63)(42,67)(43,68)(44,66)(48,70)(49,69)(51,72)(52,71)(56,73)(64,74)(65,75);(15,30)(21,45)(26,53)(31,33)(32,57)(41,66)(46,62)(47,69)(50,71)(54,63)(55,73)(58,61)(59,74)(60,75)(67,68)(70,72);(12,16,19,18)(13,22,24,39)(14,27,29,40)(15,31,30,33)(17,34,38,37)(20,42,44,43)(21,46,45,62)(23,35,49,64)(25,51,52,48)(26,54,53,63)(28,36,56,65)(32,58,57,61)(41,67,66,68)(47,59,69,74)(50,72,71,70)(55,60,73,75)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 55623);