Finite Group DatabasebetaFinite Group Databasebeta| order | 18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D631⋊C5) |
| unambiguous semidirect product | (C631⋊C5)⋊D3 |
| unambiguous semidirect product | D1893⋊C5 |
| Fitting, socle, derived, Hall | C3×C631 ⋊ C2×C5 |
| Hall | C3×C631⋊C5 ⋊ C2 |
| Hall | D1893 ⋊ C5 |
| Hall | C631⋊C5 ⋊ D3 |
| Sylow | C631 ⋊ C5×D3 |
| Sylow | C3 ⋊ D631⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C631 | C2×C5 |
| LCS | G ▷ C3×C631 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1893 |
Polycyclic presentation:
2,3,5,631|b^a=b^2,d^a=d^630,d^c=d^242204 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D631⋊C5, C2×C3⋊(D631⋊C5) |
| maximal normal subgroup of | D3×D631⋊C5, C2×C3⋊(D631⋊C5) |
| maximal quotient of | #49180993, C2×C3⋊(D631⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18930, 14);