Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60457 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C27×C4 |
| direct product | C11×#60624 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3500 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ G | |
2038 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)(23,27)(24,29)(25,40)(26,31)(28,35)(30,33)(34,46)(36,41)(37,42)(38,44)(39,50)(43,48)(45,47)(49,51);(13,16)(17,19)(20,22,33,37,26,35,25,23)(21,27,40,28,31,42,30,32)(24,34,47,49,38,48,39,36)(29,41,50,43,44,51,45,46);(12,14,15,18)(13,17,16,19)(20,23,25,35,26,37,33,22)(21,28,30,27,31,32,40,42)(24,36,39,48,38,49,47,34)(29,43,45,41,44,46,50,51);(20,24)(21,29)(22,34)(23,36)(25,39)(26,38)(27,41)(28,43)(30,45)(31,44)(32,46)(33,47)(35,48)(37,49)(40,50)(42,51);(24,38)(29,44)(34,48)(36,49)(39,47)(41,51)(43,46)(45,50)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53612);