Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18346 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18375 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3506 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
942 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,21)(15,19)(16,25)(17,20)(18,22)(23,27)(24,26)(28,29,32,34)(30,36,37,43)(31,39,41,35)(33,40,42,38);(12,14)(13,18)(15,22)(16,23)(17,24)(19,26)(20,27)(21,25)(28,30)(29,33)(31,40)(32,37)(34,42)(35,43)(36,39)(38,41);(12,15,17,16)(13,19,20,25)(14,22,24,23)(18,26,27,21)(31,41)(35,39)(36,43)(38,40);(12,15,17,16)(13,19,20,25)(14,23,24,22)(18,21,27,26)(29,34)(30,37)(35,39)(38,40)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11363);