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×#61487 |
| 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 ◁ C11×#529 ◁ G | |
1800 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)(17,19)(20,21,25,30)(22,31,34,27)(23,35,37,44)(24,29,26,39)(28,40,45,36)(32,47,49,51)(33,43,38,42)(41,50,46,48);(12,13)(14,17)(15,16)(18,19)(20,22)(21,27)(23,32)(24,38)(25,34)(26,33)(28,41)(29,43)(30,31)(35,51)(36,50)(37,49)(39,42)(40,48)(44,47)(45,46);(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);(13,16)(17,19)(20,24,25,26)(21,29,30,39)(22,33,34,38)(23,36,37,40)(27,42,31,43)(28,44,45,35)(32,48,49,50)(41,51,46,47);(12,14,15,18)(13,17,16,19)(22,34)(27,31)(32,49)(33,38)(41,46)(42,43)(47,51)(48,50)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54475);