Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23622 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C11 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| socle | C2×C11 | C2×#396 |
| prime radical | C22×C11×#41 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C11 ◁ C23×C4×C11 ◁ G | |
960 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)(12,13,18,22,17,23,16,21)(14,24,32,35,27,34,26,19)(15,20,29,36,31,37,30,38)(25,39,40,33,28,42,41,43);(12,14,16,26,17,27,18,32)(13,19,22,24,23,35,21,34)(15,28,30,40,31,25,29,41)(20,33,36,42,37,43,38,39);(12,15)(13,20)(14,25)(16,29)(17,31)(18,30)(19,33)(21,36)(22,38)(23,37)(24,39)(26,40)(27,28)(32,41)(34,42)(35,43);(12,16,17,18)(13,21,23,22)(14,26,27,32)(15,29,31,30)(19,34,35,24)(20,36,37,38)(25,40,28,41)(33,42,43,39)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16610);