Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C27 |
| direct product | C11×#20992 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#537 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C11×#41 ◁ G | |
1738 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)(16,17,21,26,22,25,20,24)(18,19,23,28,27,29,31,30);(16,18,21,31,22,27,20,23)(17,19,24,28,25,29,26,30);(13,15)(16,19)(17,23)(18,24)(20,30)(21,28)(22,29)(25,31)(26,27);(16,20,22,21)(17,24,25,26)(18,23,27,31)(19,28,29,30)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 13980);