Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33392 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C22×#102 |
| commutator | C8 | C23×C4×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C2×C11×#576 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C2×C11×#41 ◁ C2×C11×#131 ◁ G | |
1154 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)(12,13,16,21,17,23,31,22)(14,19,26,36,24,34,39,37)(15,27,29,20,30,18,28,33)(25,40,42,35,38,32,41,43);(13,18)(15,28)(16,31)(19,32)(20,21)(22,33)(23,27)(25,41)(26,39)(29,30)(34,40)(35,36)(37,43)(38,42);(12,14)(13,19)(15,25)(16,26)(17,24)(18,32)(20,35)(21,36)(22,37)(23,34)(27,40)(28,41)(29,42)(30,38)(31,39)(33,43);(14,24)(19,34)(25,38)(26,39)(32,40)(35,43)(36,37)(41,42)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26380);