Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18414 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18436 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C11×#3558 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
972 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)(14,18)(15,17)(16,20)(19,23)(21,25)(22,24)(26,27)(28,29,33,37)(30,38,40,43)(31,36,32,35)(34,41,42,39);(13,17)(15,23)(18,24)(19,20)(22,27)(25,26)(28,30)(29,34)(31,39)(32,41)(33,40)(35,38)(36,43)(37,42);(12,14)(13,18)(15,22)(16,21)(17,24)(19,26)(20,25)(23,27)(31,32)(35,36)(38,43)(39,41);(14,21)(18,25)(22,27)(24,26)(28,31,33,32)(29,35,37,36)(30,39,40,41)(34,38,42,43)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11424);