Finite Group DatabasebetaFinite Group Databasebeta| order | 18690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D623 |
| unambiguous semidirect product | C89⋊(C3×C5×D7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D623 |
| commutator, cosocle, hypocenter | C7×C89 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C7×C89 | C2 |
| LCS | G ▷ C7×C89 | |
| UCS | C1 ◁ C3×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9345 |
4695 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D7×D89, C3×D5×D623, C3×D35⋊D89, … |
| maximal normal subgroup of | C3×C5×D7×D89, C3×D5×D623, C3×D35⋊D89, … |
| maximal quotient of | C3×C5×Dic623, C2×C3×C5×D623 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18690, 5);