Finite Group DatabasebetaFinite Group Databasebeta| order | 22380 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic1865⋊C3 |
| derived, Hall | C5×C373 ⋊ C3×C4 |
| Hall | Dic1865 ⋊ C3 |
| Hall | C5×C373⋊C3 ⋊ C4 |
| Hall | C373⋊C3 ⋊ Dic5 |
| Sylow | C373 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ Dic373⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(D373⋊C3) |
| commutator, hypocenter | C5×C373 | C3×C4 |
| Fitting, socle, cosocle | C2×C5×C373 | C2×C3 |
| prime radical | C2×C5×C373⋊C3 | C2 |
| LCS | G ▷ C5×C373 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7460 |
Polycyclic presentation:
2,3,5,373,2|a^2=e,c^a=c^4,d^a=d^372,d^b=d^284644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22380, 12);