Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60717 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
1870 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,17)(15,16)(18,19)(20,21)(22,32)(23,35)(24,28)(25,30)(26,31)(27,41)(29,39)(33,47)(34,44)(36,49)(37,45)(38,50)(40,43)(42,51)(46,48);(13,16)(17,19)(20,22,26,24)(21,28,31,32)(23,33,38,36)(25,40,27,34)(29,42,45,46)(30,44,41,43)(35,49,50,47)(37,51,39,48);(20,23,27,39,26,38,25,37)(21,29,30,35,31,45,41,50)(22,33,34,48,24,36,40,51)(28,42,44,49,32,46,43,47);(12,14,15,18)(13,17,16,19)(20,24,26,22)(21,28,31,32)(23,36,38,33)(25,34,27,40)(29,42,45,46)(30,44,41,43)(35,49,50,47)(37,48,39,51);(20,25,26,27)(21,30,31,41)(22,34,24,40)(23,37,38,39)(28,43,32,44)(29,35,45,50)(33,48,36,51)(42,47,46,49)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53705);