Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24295 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24296 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2408 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
1270 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)(14,25)(15,30)(16,36)(17,40)(18,23)(19,24)(20,28)(21,34)(22,37)(26,42)(27,55)(29,44)(31,46)(32,47)(33,49)(35,48)(38,50)(39,64)(41,45)(43,57)(51,56)(52,70)(53,67)(54,68)(58,60)(59,74)(61,63)(62,71)(65,69)(66,72)(73,75);(12,14,17,28,19,29,18,41)(13,20,23,25,24,45,40,44)(15,31,33,26,35,53,34,54)(16,27,37,56,39,57,38,65)(21,46,48,68,49,67,30,42)(22,43,36,51,50,55,64,69)(32,59,60,52,62,72,61,73)(47,70,63,74,71,75,58,66);(12,15)(13,21)(14,26)(16,32)(17,33)(18,34)(19,35)(20,42)(22,47)(23,48)(24,49)(25,46)(27,52)(28,53)(29,54)(30,40)(31,41)(36,63)(37,60)(38,61)(39,62)(43,66)(44,67)(45,68)(50,71)(51,70)(55,74)(56,72)(57,73)(58,64)(59,65)(69,75);(12,16,18,38,19,39,17,37)(13,22,40,64,24,50,23,36)(14,27,41,65,29,57,28,56)(15,32,34,61,35,62,33,60)(20,43,44,69,45,55,25,51)(21,47,30,58,49,71,48,63)(26,52,31,59,54,73,53,72)(42,66,67,75,68,74,46,70)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17284);