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×#60076 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×C22⋊C4 |
| commutator | C22 | C24×C4×C11 |
| Frattini, cosocle | C2×C4 | 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 | |
4812 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)(12,13,17,23,18,22,16,21)(14,24,26,37,27,19,31,33)(15,20,30,36,28,34,29,35)(25,38,40,43,39,32,41,42);(12,14)(13,19)(15,25)(16,26)(17,31)(18,27)(20,32)(21,33)(22,24)(23,37)(28,39)(29,40)(30,41)(34,38)(35,42)(36,43);(12,15)(13,20)(14,25)(16,29)(17,30)(18,28)(19,32)(21,35)(22,34)(23,36)(24,38)(26,40)(27,39)(31,41)(33,42)(37,43);(15,28)(20,34)(25,39)(29,30)(32,38)(35,36)(40,41)(42,43);(12,16,18,17)(13,21,22,23)(14,26,27,31)(15,29,28,30)(19,33,24,37)(20,35,34,36)(25,40,39,41)(32,42,38,43)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 53064);