Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C11 · Schur multiplier (H2) = C210 |
| direct product | C11×#60070 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C23 | C25×C11 |
| socle | C2×C11 | C23×C22⋊C4 |
| prime radical | C2×C11×#585 | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C11×#41 ◁ G | |
4892 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22,25,18)(15,19)(16,20)(17,21)(23,34,36,29)(24,35,38,30)(26,31)(27,32)(28,33)(37,42,43,40)(39,41);(12,14)(13,18)(15,23)(16,24)(17,25)(19,29)(20,30)(21,22)(26,36)(27,37)(28,38)(31,34)(32,40)(33,35)(39,43)(41,42);(12,15)(13,19)(14,23)(16,27)(17,26)(18,29)(20,32)(21,31)(22,34)(24,37)(25,36)(28,39)(30,40)(33,41)(35,42)(38,43);(15,26)(19,31)(23,36)(27,39)(29,34)(32,41)(37,43)(40,42);(12,16,17,28)(13,20,21,33)(14,24,25,38)(15,27,26,39)(18,30,22,35)(19,32,31,41)(23,37,36,43)(29,40,34,42)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53058);