Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60367 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#60569 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C11×#117 ◁ G | |
2010 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)(20,21,26,31)(22,27,33,41)(23,36,38,45)(24,30,25,29)(28,39,44,37)(32,46,47,51)(34,43,35,42)(40,49,50,48);(13,16)(17,19)(20,22,26,33)(21,27,31,41)(23,32,38,47)(24,34,25,35)(28,40,44,50)(29,42,30,43)(36,46,45,51)(37,48,39,49);(20,23)(21,28)(22,32)(24,37)(25,39)(26,38)(27,40)(29,36)(30,45)(31,44)(33,47)(34,48)(35,49)(41,50)(42,46)(43,51);(12,14,15,18)(13,17,16,19)(22,33)(27,41)(32,47)(34,35)(40,50)(42,43)(46,51)(48,49);(20,24,26,25)(21,29,31,30)(22,34,33,35)(23,37,38,39)(27,42,41,43)(28,36,44,45)(32,48,47,49)(40,46,50,51)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53557);