Finite Group DatabasebetaFinite Group Databasebeta| order | 18150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C5⋊(C5⋊#10624391) |
| Fitting, socle, Hall | C52×C112 ⋊ D3 |
| derived, Hall | C52×C112⋊C3 ⋊ C2 |
| Hall | C112⋊C3 ⋊ C5⋊D5 |
| Sylow | C112 ⋊ C3⋊(C5⋊D5) |
| Sylow | C52 ⋊ #10624391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C52×C112⋊C3 | C2 |
| Fitting, socle | C52×C112 | D3 |
| LCS | G ▷ C52×C112⋊C3 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2,3,5^2,11^2|b^a=b^2,c^a=c^4,d^a=d^4,f^a=e^4f^10,e^b=e^7f^10,f^b=e^2f^3554 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C5⋊#10624391, #49137609, C5⋊D5×#10624391, … |
| maximal normal subgroup of | D5×C5⋊#10624391, #49137609, C5⋊D5×#10624391, … |
| maximal quotient of | #49137286, C2×C5⋊(C5⋊#10624391) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18150, 166);