Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33539 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33542 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#447 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3584 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
1084 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)(12,13,19,25)(14,26,30,54)(15,31,35,46)(16,24,18,22)(17,37,40,49)(20,42,45,29)(21,32,48,34)(23,36,51,39)(27,55,59,73)(28,60,41,50)(33,64,67,47)(38,52,68,44)(43,65,71,75)(53,56,74,58)(57,61,69,70)(62,63,72,66);(12,14)(13,20)(15,27)(16,28)(17,38)(18,41)(19,30)(21,43)(22,44)(23,50)(24,52)(25,45)(26,37)(29,39)(31,61)(32,56)(33,65)(34,58)(35,59)(36,42)(40,68)(46,70)(47,73)(48,71)(49,54)(51,60)(53,62)(55,64)(57,66)(63,69)(67,75)(72,74);(12,15)(13,21)(14,27)(16,32)(17,33)(18,34)(19,35)(20,43)(22,46)(23,47)(24,31)(25,48)(26,53)(28,56)(29,57)(30,59)(36,63)(37,62)(38,65)(39,66)(40,67)(41,58)(42,69)(44,70)(45,71)(49,72)(50,73)(51,64)(52,61)(54,74)(55,60)(68,75);(12,16,19,18)(13,22,25,24)(14,28,30,41)(15,32,35,34)(17,36,40,39)(20,44,45,52)(21,46,48,31)(23,49,51,37)(26,50,54,60)(27,56,59,58)(29,38,42,68)(33,63,67,66)(43,70,71,61)(47,72,64,62)(53,73,74,55)(57,65,69,75)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26530);