Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C23 |
| direct product | C11×#13404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C11 |
| prime radical | C2×C11×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ C2×C11×#131 ◁ G | |
406 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,19)(14,23)(15,17)(16,30)(20,36)(21,31)(22,28)(24,39)(25,32)(26,41)(27,40)(29,33)(34,38)(37,42);(12,13)(14,24)(15,28)(16,31)(17,19)(18,22)(20,26)(21,33)(23,38)(25,37)(27,34)(29,35)(30,43)(32,39)(36,40)(41,42);(12,14)(13,20,22,24)(15,27)(16,32)(17,25)(18,26)(19,34,28,37)(21,39,31,36)(23,30)(29,41)(33,40)(35,38,43,42)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 6392);