Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C5⋊#11925893) |
| unambiguous semidirect product | C5⋊(C3⋊#11925893) |
| Fitting, socle, derived | C3×C5×C112 ⋊ C2×C5 |
| Hall | C3×C5×#10597245 ⋊ C2 |
| Hall | C5×#10597245 ⋊ D3 |
| Hall | C3×C112 ⋊ C5×D5 |
| Sylow | C112 ⋊ C5×D15 |
| Sylow | C3 ⋊ C5⋊#11925893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C112 | C2×C5 |
| LCS | G ▷ C3×C5×C112 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2,5,3,5,11^2|c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^10,e^b=e^4,f^b=f^3225 conjugacy classes — view the full character table.
| maximal subgroup of | #11925890⋊D15, #11925896⋊D15, D15×#11925893, … |
| maximal normal subgroup of | #11925890⋊D15, #11925896⋊D15, D15×#11925893, … |
| maximal quotient of | C3⋊#27130852, C2×C3⋊(C5⋊#11925893) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 149);