Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18992 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#19007 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C22×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
862 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)(12,13,16,18)(14,20,22,27)(15,23,25,19)(17,24,26,21)(28,29,33,30)(31,38,39,43)(32,37,42,35)(34,41,36,40);(12,14)(13,17)(15,24)(16,22)(18,26)(19,27)(20,23)(21,25)(28,30,33,29)(31,36,39,34)(32,35,42,37)(38,41,43,40);(15,25)(19,23)(20,27)(21,24)(28,31)(29,34)(30,36)(32,41)(33,39)(35,43)(37,38)(40,42);(13,18)(17,26)(19,23)(20,27)374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 11995);