Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3057 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60612 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| socle | C22×C11 | C23×D4 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C11×#117 ◁ G | |
2050 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)(12,13)(14,17)(15,16)(18,19)(20,21)(22,32)(23,37)(24,29)(25,30)(26,31)(27,35)(28,39)(33,41)(34,43)(36,42)(38,45)(40,44)(46,49)(47,51)(48,50);(13,16)(17,19)(20,22,25,36,26,34,24,35)(21,27,29,43,31,42,30,32)(23,33,39,49,40,47,38,48)(28,41,37,50,45,51,44,46);(12,14,15,18)(13,17,16,19)(20,23,24,38,26,40,25,39)(21,28,30,44,31,45,29,37)(22,33,35,48,34,47,36,49)(27,41,32,46,42,51,43,50);(22,34)(27,42)(32,43)(33,47)(35,36)(41,51)(46,50)(48,49);(20,24,26,25)(21,29,31,30)(22,35,34,36)(23,38,40,39)(27,43,42,32)(28,37,45,44)(33,48,47,49)(41,50,51,46)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53600);