Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2010 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#11374 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | #127 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C23×C4 | C23×C11 |
| socle | C22×C11 | #399 |
| prime radical | C24×C11 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
598 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)(12,13)(14,15)(16,17)(18,27,31,43)(19,32)(20,25)(21,26)(22,36)(23,29,39,30)(24,35)(28,44,45,40)(33,47,46,38)(34,42)(37,41);(13,15)(16,18,22,29,21,31,20,30)(17,23,36,27,26,39,25,43)(19,33,37,45,35,46,34,28)(24,40,42,38,32,44,41,47);(13,15)(16,19,22,37,21,35,20,34)(17,24,36,42,26,32,25,41)(18,28,29,33,31,45,30,46)(23,38,27,44,39,47,43,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4362);