Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24404 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#24405 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C24 | C24×C11 |
| prime radical | C11×#3484 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C25×C11 ◁ G | |
1698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(16,17)(18,24,26,21)(19,27)(20,23)(22,28)(25,30,31,29);(12,13)(14,15)(16,18)(17,21)(19,25)(20,26)(22,29)(23,24)(27,30)(28,31);(13,15)(16,19)(17,22)(18,25)(20,28)(21,29)(23,27)(24,30)(26,31);(16,18)(17,21)(19,25)(20,26)(22,29)(23,24)(27,30)(28,31)473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 17393);