Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33340 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | C22×D4 |
| commutator | C4 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×C22⋊C8 |
| prime radical | C11×#585 | C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C2×C11×#131 ◁ G | |
1114 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)(12,13,17,23,18,24,38,51,19,25,39,52,16,22,36,49)(14,26,29,54,28,43,58,50,30,48,37,64,35,20,40,42)(15,21,33,46,34,47,63,72,31,44,59,68,32,45,61,70)(27,53,57,73,56,66,74,71,55,69,62,75,60,41,65,67);(12,14)(13,20)(15,27)(16,35)(17,37)(18,28)(19,30)(21,41)(22,48)(23,50)(24,26)(25,43)(29,39)(31,55)(32,60)(33,62)(34,56)(36,58)(38,40)(42,52)(44,66)(45,69)(46,71)(47,53)(49,54)(51,64)(57,59)(61,74)(63,65)(67,68)(70,73)(72,75);(12,15)(13,21)(14,27)(16,32)(17,33)(18,34)(19,31)(20,41)(22,45)(23,46)(24,47)(25,44)(26,53)(28,56)(29,57)(30,55)(35,60)(36,61)(37,62)(38,63)(39,59)(40,65)(42,67)(43,66)(48,69)(49,70)(50,71)(51,72)(52,68)(54,73)(58,74)(64,75);(15,31)(21,44)(27,55)(32,34)(33,59)(41,66)(45,47)(46,68)(53,69)(56,60)(57,62)(61,63)(65,74)(67,71)(70,72)(73,75)968 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26328);