Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C25 |
| direct product | C11×#24797 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C11 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ G | |
894 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15)(16,17,20,23)(18,25,28,31)(19,24,26,22)(21,29,30,27);(16,17,19,22,20,23,26,24)(18,21,27,25,28,30,29,31);(13,15)(16,17)(18,21)(19,22)(20,23)(24,26)(25,27)(28,30)(29,31);(16,18,26,29,20,28,19,27)(17,21,24,31,23,30,22,25)506 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17785);