Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#23585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C11×#117 ◁ G | |
1122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1408 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,21)(19,20)(22,23)(24,25,29,34)(26,35,27,31)(28,33,30,38)(32,36,39,37);(12,13)(14,15)(17,20)(21,23)(24,26)(25,31)(27,29)(28,37)(30,36)(32,38)(33,39)(34,35);(13,15)(24,27,29,26)(25,32,34,39)(28,37,30,36)(31,33,35,38);(16,18,19,22)(17,21,20,23)(24,28,29,30)(25,33,34,38)(26,36,27,37)(31,32,35,39)572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 16573);