Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61629 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61665 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#532 ◁ G | |
2008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21,26,30)(22,27,33,43)(23,34,36,44)(24,29,25,38)(28,39,45,35)(31,46,49,51)(32,41,37,42)(40,47,50,48);(12,14)(13,16)(15,19)(17,18)(20,22)(21,27)(23,31)(24,37)(25,32)(26,33)(28,40)(29,42)(30,43)(34,46)(35,48)(36,49)(38,41)(39,47)(44,51)(45,50);(20,23,26,36)(21,28,30,45)(22,31,33,49)(24,35,25,39)(27,40,43,50)(29,44,38,34)(32,47,37,48)(41,46,42,51);(14,19)(16,18)(20,22)(21,27)(23,31)(24,37)(25,32)(26,33)(28,40)(29,42)(30,43)(34,46)(35,48)(36,49)(38,41)(39,47)(44,51)(45,50);(13,17)(16,18)(20,24,26,25)(21,29,30,38)(22,32,33,37)(23,35,36,39)(27,41,43,42)(28,44,45,34)(31,47,49,48)(40,46,50,51)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54653);