Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#33337 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C11 |
| Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C2×C11 | C22×C22⋊C8 |
| prime radical | C22×C11×#41 | C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C2×C11×#131 ◁ G | |
1128 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)(12,13,15,20,16,21,26,33,17,18,25,29,27,30,37,40)(14,19,23,31,24,32,36,41,22,28,34,38,35,39,42,43);(13,18)(15,25)(19,28)(21,30)(23,34)(26,37)(32,39)(36,42);(12,14)(13,19)(15,23)(16,24)(17,22)(18,28)(20,31)(21,32)(25,34)(26,36)(27,35)(29,38)(30,39)(33,41)(37,42)(40,43);(14,22)(19,28)(23,34)(24,35)(31,38)(32,39)(36,42)(41,43)902 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26325);