Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C25⋊#10624391 |
| Fitting, Hall | C112×C25 ⋊ D3 |
| derived, Hall | C25×C112⋊C3 ⋊ C2 |
| Hall | C112⋊C3 ⋊ D25 |
| Sylow | C112 ⋊ D75 |
| Sylow | C25 ⋊ #10624391 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C25×C112⋊C3 | C2 |
| Frattini | C5 | C5⋊#10624391 |
| Fitting | C112×C25 | D3 |
| socle | C5×C112 | D15 |
| LCS | G ▷ C25×C112⋊C3 | |
| UCS | C1 | |
39 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2,3,5,11^2,5|c^5=f^4,b^a=b^2,c^a=c^4f,e^a=d^4e^10,f^a=f^4,d^b=d^7e^10,e^b=d^2e^3554 conjugacy classes — view the full character table.
| maximal subgroup of | #10624391⋊D25, ((C11⋊D11)⋊C3)⋊D25, D25×#10624391, … |
| maximal normal subgroup of | #10624391⋊D25, ((C11⋊D11)⋊C3)⋊D25, D25×#10624391, … |
| maximal quotient of | #49137049, C2×C25⋊#10624391 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 71);