Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(C5⋊#11925890) |
| unambiguous semidirect product | C5⋊(C3⋊#11925890) |
| Fitting, socle | C3×C5×C112 ⋊ D5 |
| derived, Hall | C3×C5×#10597245 ⋊ C2 |
| Hall | C5×#10597245 ⋊ D3 |
| Hall | C3×C112 ⋊ C5⋊D5 |
| Sylow | C112 ⋊ C3⋊(C5⋊D5) |
| Sylow | C3 ⋊ C5⋊#11925890 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×#10597245 | C2 |
| Fitting, socle | C3×C5×C112 | D5 |
| LCS | G ▷ C3×C5×#10597245 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
Polycyclic presentation:
2,3,5^2,11^2|b^a=b^2,c^a=c^4,d^a=d^4,e^a=e^3f^3,f^a=ef^8,e^c=e^4f^8,f^c=f^3234 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#11925890, #11925890⋊D15, #49137460, … |
| maximal normal subgroup of | D15×#11925890, #11925890⋊D15, #49137460, … |
| maximal quotient of | C3⋊#27130863, C2×C3⋊(C5⋊#11925890) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 160);