Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C5⋊#64418) |
| unambiguous semidirect product | C5⋊(C3⋊#64418) |
| Fitting, socle | C3×C5×C72 ⋊ D3 |
| derived, Hall | C3×C5×#3862 ⋊ C2 |
| Hall | C3×#3862 ⋊ D5 |
| Hall | C5×C72 ⋊ C3⋊D3 |
| Sylow | C72 ⋊ C3⋊D15 |
| Sylow | C5 ⋊ C3⋊#64418 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×#3862 | C2 |
| Fitting, socle | C3×C5×C72 | D3 |
| LCS | G ▷ C3×C5×#3862 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
Polycyclic presentation:
2,3^2,5,7^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^b=e^4,f^b=f^2153 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊(C25⋊#64418), C5×C3⋊(C5⋊#64418), C3⋊(C5⋊(C5⋊#64418)) |
| maximal normal subgroup of | C5×C3⋊(C5⋊#64418) |
| maximal quotient of | C3⋊(C25⋊#64418), C5×C3⋊(C5⋊#64418), C3⋊(C5⋊(C5⋊#64418)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 116);