Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61643 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#61649 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| prime radical | C11×#3485 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#525 ◁ G | |
2042 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)(14,18)(15,17)(16,19)(20,21,26,31)(22,27,34,42)(23,35,37,45)(24,30,25,29)(28,39,43,36)(32,46,48,50)(33,44,38,41)(40,47,51,49);(12,14)(13,16)(15,19)(17,18)(20,22,26,34)(21,27,31,42)(23,32,37,48)(24,38,25,33)(28,40,43,51)(29,44,30,41)(35,46,45,50)(36,49,39,47);(20,23)(21,28)(22,32)(24,36)(25,39)(26,37)(27,40)(29,35)(30,45)(31,43)(33,47)(34,48)(38,49)(41,50)(42,51)(44,46);(14,19)(16,18)(20,24,26,25)(21,29,31,30)(22,33,34,38)(23,36,37,39)(27,41,42,44)(28,35,43,45)(32,47,48,49)(40,50,51,46);(13,17)(16,18)(22,34)(27,42)(32,48)(33,38)(40,51)(41,44)(46,50)(47,49)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54637);