Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2121 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33347 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C2×#99 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C2×D4 | C24×C11 |
| socle | C2×C11 | C22×#99 |
| prime radical | C11×#3449 | C2 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C22×C4×C11 ◁ C22×C11×#41 ◁ G | |
1236 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)(15,19)(16,28,29,20)(17,21)(18,25,30,37)(23,34)(24,35)(26,39,40,32)(27,33)(31,38,41,43)(36,42);(12,14)(13,18)(15,24)(16,25)(17,23)(19,31)(20,22)(21,30)(26,38)(27,36)(28,34)(29,37)(32,35)(33,41)(39,42)(40,43);(14,23)(18,30)(22,34)(24,36)(25,37)(31,41)(35,42)(38,43);(12,15,17,27)(13,19,21,33)(14,24,23,36)(16,26,29,40)(18,31,30,41)(20,32,28,39)(22,35,34,42)(25,38,37,43)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26335);