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×#33414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×#107 |
| prime radical | C2×C11×#41 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
622 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)(12,13,17,23,19,24,18,39)(14,25,29,50,31,51,30,59)(15,21,34,46,32,44,35,63)(16,36,37,47,38,64,26,22)(20,40,42,58,43,52,49,28)(27,48,56,71,54,69,57,74)(33,61,62,68,60,75,53,45)(41,65,67,73,66,72,70,55);(12,14,26,52,18,30,38,58,19,31,37,40,17,29,16,28)(13,20,36,50,23,42,47,51,24,43,64,59,39,49,22,25)(15,27,53,72,35,57,60,73,32,54,62,65,34,56,33,55)(21,41,61,71,46,67,68,69,44,66,75,74,63,70,45,48);(12,15)(13,21)(14,27)(16,33)(17,34)(18,35)(19,32)(20,41)(22,45)(23,46)(24,44)(25,48)(26,53)(28,55)(29,56)(30,57)(31,54)(36,61)(37,62)(38,60)(39,63)(40,65)(42,67)(43,66)(47,68)(49,70)(50,71)(51,69)(52,72)(58,73)(59,74)(64,75);(15,32)(21,44)(27,54)(33,60)(34,35)(41,66)(45,68)(46,63)(48,69)(53,62)(55,73)(56,57)(61,75)(65,72)(67,70)(71,74)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26402);