Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#23527 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#124 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#394 |
| prime radical | C2×C11×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22)(15,26)(16,30)(17,21)(18,24)(19,28)(20,32)(23,37)(25,36)(27,41)(29,35)(31,34)(33,38)(39,42)(40,43);(12,14)(13,18)(15,27)(16,31)(17,25)(19,33)(20,36)(21,34)(22,30)(23,28)(24,32)(26,39)(29,38)(35,41)(37,40)(42,43);(12,15,16,29,17,28,32,43)(13,19,20,35,21,26,30,40)(14,23,24,38,25,27,31,42)(18,33,22,37,34,39,36,41);(15,28)(19,26)(23,27)(29,43)(33,39)(35,40)(37,41)(38,42)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16515);