Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #20338 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#33329 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×C42 |
| commutator | C4 | C22×C42×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×#97 |
| prime radical | C2×C11×#41 | C2×C4 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ G | |
716 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)(12,13,15,20,16,22,27,35,17,21,26,36,28,18,29,31)(14,19,24,33,25,34,39,43,23,32,37,42,38,30,40,41);(13,18,21,22)(15,26)(19,30,32,34)(20,35,36,31)(24,37)(27,29)(33,43,42,41)(39,40);(12,14)(13,19)(15,24)(16,25)(17,23)(18,30)(20,33)(21,32)(22,34)(26,37)(27,39)(28,38)(29,40)(31,41)(35,43)(36,42);(14,23)(19,32)(24,37)(25,38)(30,34)(33,42)(39,40)(41,43)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26317);