Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#32952 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#585 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1266 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)(12,13,19,25)(14,26,31,42)(15,32,35,48)(16,22,37,47)(17,24,18,23)(20,30,43,29)(21,38,45,34)(27,52,55,40)(28,51,57,68)(33,61,64,60)(36,49,39,46)(41,59,66,56)(44,62,69,63)(50,58,67,54)(53,65,74,71)(70,72,75,73);(12,14,18,30,19,31,17,29)(13,20,24,42,25,43,23,26)(15,27,38,58,35,55,34,54)(16,28,39,59,37,57,36,56)(21,40,48,67,45,52,32,50)(22,41,49,68,47,66,46,51)(33,53,63,73,64,74,62,72)(44,65,61,75,69,71,60,70);(12,15)(13,21)(14,27)(16,33)(17,34)(18,38)(19,35)(20,40)(22,44)(23,32)(24,48)(25,45)(26,50)(28,53)(29,54)(30,58)(31,55)(36,62)(37,64)(39,63)(41,65)(42,67)(43,52)(46,60)(47,69)(49,61)(51,70)(56,72)(57,74)(59,73)(66,71)(68,75);(12,16)(13,22)(14,28)(15,33)(17,36)(18,39)(19,37)(20,41)(21,44)(23,46)(24,49)(25,47)(26,51)(27,53)(29,56)(30,59)(31,57)(32,60)(34,62)(35,64)(38,63)(40,65)(42,68)(43,66)(45,69)(48,61)(50,70)(52,71)(54,72)(55,74)(58,73)(67,75)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 25940);