Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C3⋊D615 |
| unambiguous semidirect product | C3⋊(C5×D615) |
| unambiguous semidirect product | C5⋊(C5×C3⋊D123) |
| Fitting, socle, Hall | C32×C52×C41 ⋊ C2 |
| derived | C32×C5×C41 ⋊ C2×C5 |
| Hall | C52×C41 ⋊ C3⋊D3 |
| Hall | C32×C41 ⋊ C5×D5 |
| Hall | C32×C52 ⋊ D41 |
| Sylow | C41 ⋊ C5×C3⋊D15 |
| Sylow | C52 ⋊ C3⋊D123 |
| Sylow | C32 ⋊ C5×D205 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C3⋊D615 |
| commutator, cosocle, hypocenter | C32×C5×C41 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C2 |
| LCS | G ▷ C32×C5×C41 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3690 |
4620 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20301653, C5×#20301654, #49147069, … |
| maximal normal subgroup of | C5×#20301653, C5×#20301654, #49147069, … |
| maximal quotient of | C5×C3⋊Dic615, C2×C5×C3⋊D615 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 84);