Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D363 |
| unambiguous semidirect product | C3⋊(C52×D121) |
| Fitting, Hall | C3×C52×C121 ⋊ C2 |
| derived, Hall | C3×C121 ⋊ C2×C52 |
| Hall | C52×C121 ⋊ D3 |
| Sylow | C121 ⋊ C52×D3 |
| Hall | C3×C52 ⋊ D121 |
| Sylow | C3 ⋊ C52×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D363 |
| commutator, cosocle, hypocenter | C3×C121 | C2×C52 |
| Frattini | C11 | C52×D33 |
| Fitting | C3×C52×C121 | C2 |
| socle | C3×C52×C11 | D11 |
| LCS | G ▷ C3×C121 | |
| UCS | C1 ◁ C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
4575 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D121, C5×D5×D363, C5×D15⋊D121, … |
| maximal normal subgroup of | C52×D3×D121, C5×D5×D363, C5×D15⋊D121, … |
| maximal quotient of | C52×Dic363, C2×C52×D363 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 34);