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×#60720 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C4×C11×#41 ◁ 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)(22,26,31,40)(23,33,36,50)(24,37,38,28)(27,42,44,35)(30,45,34,49)(32,48,47,41)(39,51,43,46);(13,16)(17,19)(20,22)(21,26)(23,34)(24,32)(25,31)(27,43)(28,41)(29,40)(30,36)(33,49)(35,51)(37,48)(38,47)(39,44)(42,46)(45,50);(20,23,24,35,25,36,38,42)(21,27,28,33,29,44,37,50)(22,30,32,46,31,34,47,51)(26,39,41,45,40,43,48,49);(12,14,15,18)(13,17,16,19)(20,22)(21,26)(23,30)(24,32)(25,31)(27,39)(28,41)(29,40)(33,45)(34,36)(35,46)(37,48)(38,47)(42,51)(43,44)(49,50);(22,31)(26,40)(30,34)(32,47)(39,43)(41,48)(45,49)(46,51)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53708);