Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C11⋊D11)⋊C3)⋊C25 |
| unambiguous semidirect product | #20258402⋊C3 |
| derived, Sylow | C112 ⋊ C2×C3×C25 |
| Hall | (C112⋊C3)⋊C25 ⋊ C2 |
| Hall | #20258402 ⋊ C3 |
| Hall | #15690027 ⋊ C2×C3 |
| Hall | (C11⋊D11)⋊C3 ⋊ C25 |
| Hall | C112⋊C3 ⋊ C2×C25 |
| Hall | C11⋊D11 ⋊ C3×C25 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C5 | ((C11⋊D11)⋊C3)⋊C5 |
| commutator, hypocenter | C112 | C2×C3×C25 |
| Fitting, socle, cosocle | C5×C112 | C2×C3×C5 |
| prime radical | C5×(C11⋊D11)⋊C3 | C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C5 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2,3,5,11^2,5|c^5=f,d^a=d^10,e^a=e^10,d^b=d^3e^9,e^b=de^7,d^c=d^4,e^c=e^4170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 41);