Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61049 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61331 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3045 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#533 ◁ G | |
1764 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,16)(17,18)(20,21)(22,31)(23,35)(24,29)(25,30)(26,39)(27,33)(28,36)(32,47)(34,43)(37,44)(38,42)(40,45)(41,49)(46,50)(48,51);(12,13,15,16)(14,18,19,17)(20,22,25,33)(21,27,30,31)(23,32,37,48)(24,38,26,34)(28,41,45,46)(29,43,39,42)(35,51,44,47)(36,50,40,49);(20,23)(21,28)(22,32)(24,36)(25,37)(26,40)(27,41)(29,44)(30,45)(31,46)(33,48)(34,49)(35,39)(38,50)(42,51)(43,47);(12,14,15,19)(13,17,16,18)(22,33)(27,31)(32,48)(34,38)(41,46)(42,43)(47,51)(49,50);(20,24,25,26)(21,29,30,39)(22,34,33,38)(23,36,37,40)(27,42,31,43)(28,44,45,35)(32,49,48,50)(41,51,46,47)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54319);