Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C2×C42 |
| direct product | C11×#23312 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C24 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C23×C11 | C23×C4 |
| prime radical | C11×#2388 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
912 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,17)(16,19)(20,21)(22,24)(23,25)(26,27)(28,29,32,35,31,33,38,40)(30,34,37,41,36,39,42,43);(12,14)(13,16)(15,19)(17,18)(20,22)(21,24)(23,26)(25,27)(29,33)(30,36)(35,40)(37,42);(14,19)(16,18)(21,25)(22,26)(28,30)(29,34)(31,36)(32,37)(33,39)(35,41)(38,42)(40,43);(13,17)(14,19)(21,25)(24,27)(29,33)(30,36)(35,40)(37,42)704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16300);