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×#18975 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
810 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)(14,21)(15,19)(16,24)(17,20)(18,22)(23,26)(25,27)(28,29,33,35)(30,37,34,42)(31,39,40,38)(32,41,43,36);(12,14,17,23)(13,18,20,27)(15,22,16,25)(19,26,24,21)(28,30,33,34)(29,31,35,40)(32,39,43,38)(36,42,41,37);(12,13)(14,18)(15,24)(16,19)(17,20)(21,22)(23,27)(25,26)(28,31)(29,34)(30,35)(32,42)(33,40)(36,38)(37,43)(39,41);(12,15,17,16)(13,19,20,24)(14,22,23,25)(18,26,27,21)(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, 11963);