Finite Group DatabasebetaFinite Group Databasebeta| order | 18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (D631⋊C3)⋊C5 |
| unambiguous semidirect product | (D631⋊C5)⋊C3 |
| unambiguous semidirect product | ((C631⋊C3)⋊C5)⋊C2 |
| Fitting, socle, derived, Sylow | C631 ⋊ C2×C3×C5 |
| Hall | (C631⋊C3)⋊C5 ⋊ C2 |
| Hall | D631⋊C5 ⋊ C3 |
| Hall | D631⋊C3 ⋊ C5 |
| Hall | C631⋊C5 ⋊ C2×C3 |
| Hall | C631⋊C3 ⋊ C2×C5 |
| Hall | D631 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C631 | C2×C3×C5 |
| LCS | G ▷ C631 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 631 |
Polycyclic presentation:
2,3,5,631|d^a=d^630,d^b=d^587,d^c=d^24251 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(D631⋊C3)⋊C5 |
| maximal normal subgroup of | C2×(D631⋊C3)⋊C5 |
| maximal quotient of | #49180997, C2×(D631⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18930, 18);