Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33657 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C24 |
| direct product | C11×#33657 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | C2×#481 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| prime radical | C11×#3058 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
566 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)(14,22)(15,25)(16,28)(18,31)(20,35)(21,34)(23,39)(24,27)(26,41)(29,42)(30,40)(32,38)(33,36)(37,43);(12,13)(14,18)(15,26)(16,21)(17,19)(20,29)(22,38)(23,32)(24,33)(25,41)(27,43)(28,34)(30,37)(31,39)(35,42)(36,40);(12,14,16,30,17,23,28,24)(13,18,21,37,19,32,34,33)(15,27,25,39,29,40,42,22)(20,36,35,38,26,43,41,31);(13,19)(18,32)(20,26)(21,34)(31,38)(33,37)(35,41)(36,43)440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 26645);