Finite Group DatabasebetaFinite Group Databasebeta| order | 22020 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C367⋊C3)⋊Dic5 |
| unambiguous semidirect product | Dic1835⋊C3 |
| derived, Hall | C5×C367 ⋊ C3×C4 |
| Hall | Dic1835 ⋊ C3 |
| Hall | C5×C367⋊C3 ⋊ C4 |
| Hall | C367⋊C3 ⋊ Dic5 |
| Sylow | C367 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ (C367⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D367⋊C3) |
| commutator, hypocenter | C5×C367 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C367 | C2×C3 |
| prime radical | C2×C5×C367⋊C3 | C2 |
| LCS | G ▷ C5×C367 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7340 |
Polycyclic presentation:
2,3,5,367,2|a^2=e,c^a=c^4,d^a=d^366,d^b=d^283634 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22020, 12);