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×#33458 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#117 ◁ C11×#405 ◁ G | |
646 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 79 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,15,14)(16,17)(18,28)(19,24)(20,36)(21,41)(22,25)(23,30)(26,39)(27,38)(29,53)(31,60)(32,54)(33,48)(34,63)(35,66)(37,51)(40,52)(42,50)(43,56)(44,59)(45,68)(46,65)(47,62)(49,58)(55,75)(57,78)(61,74)(64,73)(67,71)(69,79)(70,76)(72,77);(16,18,22,32)(17,23,25,44)(19,29,33,55)(20,37,40,68)(21,42,38,31)(24,43,48,70)(26,50,49,60)(27,51,41,45)(28,52,54,36)(30,58,59,39)(34,64,61,79)(35,67,62,57)(46,71,72,78)(47,73,66,69)(53,74,75,63)(56,77,76,65);(12,14,15,13)(16,19,22,33)(17,24,25,48)(18,29,32,55)(20,34,40,61)(21,35,38,62)(23,43,44,70)(26,46,49,72)(27,47,41,66)(28,53,54,75)(30,56,59,76)(31,57,42,67)(36,63,52,74)(37,64,68,79)(39,65,58,77)(45,69,51,73)(50,71,60,78);(17,25)(19,33)(23,44)(26,49)(27,41)(28,54)(29,55)(34,61)(35,62)(36,52)(45,51)(50,60)(56,76)(57,67)(64,79)(65,77)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26446);