Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20258402 |
| derived, Hall | C3×C112 ⋊ C2×C25 |
| Hall | C3×#15690027 ⋊ C2 |
| Hall | #15690027 ⋊ D3 |
| Hall | C3⋊(C11⋊D11) ⋊ C25 |
| Sylow | C112 ⋊ D3×C25 |
| Sylow | C3 ⋊ #20258402 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | C3⋊#11925892 |
| commutator, hypocenter | C3×C112 | C2×C25 |
| Fitting, socle, cosocle | C3×C5×C112 | C2×C5 |
| prime radical | C5×C3⋊(C11⋊D11) | C5 |
| LCS | G ▷ C3×C112 | |
| UCS | C1 ◁ C5 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9075 |
Polycyclic presentation:
2,5,3,11^2,5|b^5=f,c^a=c^2,d^a=d^10,e^a=e^10,d^b=d^4,e^b=e^4255 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#20258402, #20258405⋊D3, C2×C3⋊#20258402 |
| maximal normal subgroup of | D3×#20258402, #20258405⋊D3, C2×C3⋊#20258402 |
| maximal quotient of | C3⋊#27130776, C2×C3⋊#20258402 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 56);