Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33409 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C24×C11 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ C23×C8×C11 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17)(18,27)(19,24)(20,34)(21,36)(22,26)(23,31)(25,28)(29,40)(30,41)(32,46)(33,39)(35,47)(37,44)(38,45)(42,43);(16,18,28,43,21,32,35,44,22,29,33,45,19,30,20,31)(17,23,34,41,24,38,39,40,26,37,47,46,36,42,25,27);(18,29)(23,37)(27,40)(30,32)(31,44)(38,42)(41,46)(43,45);(16,19,22,21)(17,24,26,36)(18,30,29,32)(20,33,35,28)(23,38,37,42)(25,34,39,47)(27,41,40,46)(31,45,44,43)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26397);