Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#18933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3544 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
858 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,23)(16,18)(17,22)(19,24)(21,27)(25,26)(28,29,33,35)(30,37,34,42)(31,39,40,38)(32,41,43,36);(15,24)(19,23)(20,27)(22,25)(28,30,33,34)(29,31,35,40)(32,39,43,38)(36,42,41,37);(12,14)(13,17)(15,25)(16,21)(18,26)(19,27)(20,23)(22,24)(28,31)(29,34)(30,35)(32,42)(33,40)(36,38)(37,43)(39,41);(13,18)(17,26)(19,23)(20,27)(29,35)(31,40)(36,41)(37,42)407 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11921);