Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60711 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3054 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
1846 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)(20,21,25,29)(22,30,31,43)(23,27,35,41)(24,37,32,28)(26,38,39,34)(33,44,45,51)(36,48,46,42)(40,49,50,47);(13,16)(17,19)(22,31)(26,39)(30,43)(33,45)(34,38)(40,50)(44,51)(47,49);(20,22,32,38,25,31,24,34)(21,26,37,43,29,39,28,30)(23,33,46,49,35,45,36,47)(27,40,48,51,41,50,42,44);(12,14,15,18)(13,17,16,19)(20,23)(21,27)(22,33)(24,36)(25,35)(26,40)(28,42)(29,41)(30,44)(31,45)(32,46)(34,47)(37,48)(38,49)(39,50)(43,51);(23,35)(27,41)(33,45)(36,46)(40,50)(42,48)(44,51)(47,49)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53699);