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) = C25 |
| direct product | C11×#11084 |
| 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 | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G | |
878 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)(16,17,21,26,22,27,20,25)(18,23,31,39,29,37,30,38)(19,24,34,42,33,41,35,43)(28,44,32,47,45,36,46,40);(12,13,14,15)(16,18)(17,23)(19,32,33,46)(20,30)(21,31)(22,29)(24,40,41,47)(25,38)(26,39)(27,37)(28,34,45,35)(36,42,44,43);(16,19)(17,24)(18,28)(20,35)(21,34)(22,33)(23,36)(25,43)(26,42)(27,41)(29,45)(30,46)(31,32)(37,44)(38,47)(39,40)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 4072);