Finite Group DatabasebetaFinite Group Databasebeta| order | 2816 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3019 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26 |
| direct product | C11×#21475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator | C2×C4 | C23×C4×C11 |
| Frattini, cosocle | C22×C4 | C24×C11 |
| prime radical | C2×C11×#454 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
1370 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)(12,13,15,14)(17,21)(19,26)(22,30)(23,27)(25,28)(29,31);(16,17)(18,22)(19,27)(20,23)(21,26)(24,31)(25,29)(28,30);(16,18,20,24)(17,22,23,31)(19,28,26,25)(21,29,27,30);(12,14,15,13)(18,24)(22,31)(25,28)(29,30)638 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2816, 14463);