Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23522 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G | |
1326 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)(18,26)(19,30)(20,34)(21,24)(22,28)(23,33)(25,36)(27,43)(29,41)(31,42)(32,40)(35,38)(37,46)(39,44)(45,47);(16,18,21,29)(17,22,24,38)(19,31,33,27)(20,35,36,28)(23,39,30,37)(25,41,34,26)(32,44,47,46)(40,42,45,43);(13,15)(16,19,20,32,21,33,36,47)(17,23,25,40,24,30,34,45)(18,27,28,44,29,31,35,46)(22,37,26,42,38,39,41,43);(17,24)(22,38)(23,30)(25,34)(26,41)(37,39)(40,45)(42,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16510);