Finite Group DatabasebetaFinite Group Databasebeta| order | 28820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C131⋊C5)⋊Dic11 |
| derived, Hall | C11×C131 ⋊ C4×C5 |
| Hall | C11×C131⋊C5 ⋊ C4 |
| Hall | Dic1441 ⋊ C5 |
| Hall | C131⋊C5 ⋊ Dic11 |
| Sylow | C131 ⋊ C5×Dic11 |
| Sylow | C11 ⋊ Dic131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C131⋊C5)⋊D11 |
| commutator, hypocenter | C11×C131 | C4×C5 |
| Fitting, socle, cosocle | C2×C11×C131 | C2×C5 |
| prime radical | C2×C11×C131⋊C5 | C2 |
| LCS | G ▷ C11×C131 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5764 |
Polycyclic presentation:
2,5,11,131,2|a^2=e,c^a=c^10,d^a=d^130,d^b=d^53356 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28820, 27);