Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C25×C4 |
| direct product | C11×#33358 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#99 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| socle | C2×C11 | C22×#99 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G | |
1252 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)(14,22,23,35)(15,19)(16,28,30,20)(17,21)(18,25)(24,36,37,43)(26,39,41,33)(27,34)(29,31)(32,38)(40,42);(12,14)(13,18)(15,24)(16,29)(17,23)(19,32)(20,35)(21,31)(22,28)(25,30)(26,40)(27,37)(33,43)(34,42)(36,39)(38,41);(14,23)(18,31)(22,35)(24,37)(25,29)(32,42)(36,43)(38,40);(12,15,17,27)(13,19,21,34)(14,24,23,37)(16,26,30,41)(18,32,31,42)(20,33,28,39)(22,36,35,43)(25,38,29,40)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26346);