Finite Group DatabasebetaFinite Group Databasebeta| order | 18930 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C631 · Schur multiplier (H2) = C1 |
| direct product | C3×D5×C631 |
| unambiguous semidirect product | C5⋊(C2×C3×C631) |
| Fitting, socle, Hall | C3×C5×C631 ⋊ C2 |
| derived, Sylow | C5 ⋊ C2×C3×C631 |
| Hall | C5×C631 ⋊ C2×C3 |
| Hall | C3×C5 ⋊ C2×C631 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C631 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C3×C631 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C631 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C631 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9465 |
7572 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AGL(1,𝔽5)×C631, C3×C631⋊AGL(1,𝔽5), C3×D5×D631, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×C631, C3×C631⋊AGL(1,𝔽5), C3×D5×D631, … |
| maximal quotient of | C3×Dic5×C631, C2×C3×D5×C631 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18930, 6);