Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61058 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#61083 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C11 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C11×#532 ◁ G | |
2674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,22,27)(18,28,32,43)(19,24,34,41)(20,26,21,25)(23,36,39,31)(29,44,47,38)(30,45,46,37)(33,42,35,40);(16,18,22,32)(17,23,27,39)(19,29,34,47)(20,31,21,36)(24,37,41,45)(25,28,26,43)(30,35,46,33)(38,42,44,40);(13,15)(16,19)(17,24)(18,29)(20,35)(21,33)(22,34)(23,37)(25,42)(26,40)(27,41)(28,44)(30,36)(31,46)(32,47)(38,43)(39,45);(16,19)(17,24)(18,30)(20,33)(21,35)(22,34)(23,38)(25,40)(26,42)(27,41)(28,45)(29,36)(31,47)(32,46)(37,43)(39,44);(16,20,22,21)(17,25,27,26)(18,31,32,36)(19,33,34,35)(23,28,39,43)(24,40,41,42)(29,30,47,46)(37,38,45,44)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 54071);