Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2190 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#13026 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #447 |
| commutator | C2×C8 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G | |
486 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,25,35,44,36,45,22,27,19,24,21,26,37,46)(18,28,30,40,38,43,33,23,32,39,29,47,31,42,34,41);(12,13,14,15)(16,18)(17,23)(19,33)(20,34)(21,38)(22,32)(24,42)(25,43)(26,47)(27,41)(28,45)(29,36)(30,37)(31,35)(39,46)(40,44);(16,18)(17,23)(19,34)(20,33)(21,38)(22,32)(24,43)(25,42)(26,47)(27,41)(28,46)(29,37)(30,36)(31,35)(39,45)(40,44)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6014);