Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊D605) |
| unambiguous semidirect product | C5⋊D1815 |
| unambiguous semidirect product | C121⋊(C3⋊(C5⋊D5)) |
| Fitting, derived, Hall | C3×C52×C121 ⋊ C2 |
| Hall | C52×C121 ⋊ D3 |
| Hall | C3×C121 ⋊ C5⋊D5 |
| Sylow | C121 ⋊ C3⋊(C5⋊D5) |
| Hall | C3×C52 ⋊ D121 |
| Sylow | C52 ⋊ D363 |
| Sylow | C3 ⋊ C5⋊D605 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C52×C121 | C2 |
| Frattini | C11 | C3⋊(C5⋊D55) |
| socle | C3×C52×C11 | D11 |
| LCS | G ▷ C3×C52×C121 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
Polycyclic presentation:
2,3,5^2,11^2|e^11=f^10,b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^10f,f^a=f^104539 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊(C5⋊D5)×D121, C5⋊D5×D363, D3×C5⋊D605, … |
| maximal normal subgroup of | C3⋊(C5⋊D5)×D121, C5⋊D5×D363, D3×C5⋊D605, … |
| maximal quotient of | C3⋊(C121⋊#1039), C2×C3⋊(C5⋊D605) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 38);