Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24420 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24423 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3586 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1284 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)(12,13,19,41,18,23,17,24)(14,25,39,44,29,20,28,50)(15,30,40,21,33,51,34,47)(16,35,37,48,38,22,36,49)(26,54,60,52,56,45,31,42)(27,43,58,69,59,53,57,68)(32,61,65,66,63,71,64,46)(55,73,62,67,74,70,75,72);(12,14,18,29)(13,20,23,25)(15,31,33,60)(16,27,38,59)(17,39,19,28)(21,45,47,54)(22,43,35,53)(24,50,41,44)(26,40,56,34)(30,42,51,52)(32,62,63,75)(36,58,37,57)(46,70,66,73)(48,69,49,68)(55,64,74,65)(61,67,71,72);(12,15)(13,21)(14,26)(16,32)(17,40)(18,33)(19,34)(20,42)(22,46)(23,47)(24,51)(25,52)(27,55)(28,60)(29,56)(30,41)(31,39)(35,66)(36,65)(37,64)(38,63)(43,67)(44,54)(45,50)(48,61)(49,71)(53,72)(57,62)(58,75)(59,74)(68,70)(69,73);(12,16)(13,22)(14,27)(15,32)(17,37)(18,38)(19,36)(20,43)(21,46)(23,35)(24,49)(25,53)(26,55)(28,58)(29,59)(30,61)(31,62)(33,63)(34,65)(39,57)(40,64)(41,48)(42,67)(44,69)(45,70)(47,66)(50,68)(51,71)(52,72)(54,73)(56,74)(60,75)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17411);