Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C5×C41×D45 |
| unambiguous semidirect product | C5⋊(C5×D9×C41) |
| unambiguous semidirect product | C9⋊(C5×D5×C41) |
| Fitting, Hall | C52×C9×C41 ⋊ C2 |
| derived | C5×C9 ⋊ C2×C5×C41 |
| Hall | C52×C41 ⋊ D9 |
| Hall | C9×C41 ⋊ C5×D5 |
| Hall | C52×C9 ⋊ C2×C41 |
| Sylow | C52 ⋊ D9×C41 |
| Sylow | C9 ⋊ C5×D5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C41 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C2×C5×C41 |
| Frattini | C3 | C5×D15×C41 |
| Fitting | C52×C9×C41 | C2 |
| socle | C3×C52×C41 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C5×C41 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3690 |
4920 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D41×D45, C5×D5×D9×C41, C5×D45⋊D41, … |
| maximal normal subgroup of | C5×D41×D45, C5×D5×D9×C41, C5×D45⋊D41, … |
| maximal quotient of | C5×C41×Dic45, C2×C5×C41×D45 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 53);