Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C5⋊#64425 |
| unambiguous semidirect product | C5⋊(C3×#64425) |
| Fitting, socle | C3×C5×C72 ⋊ C2×C3 |
| derived, Hall | C5×C72 ⋊ C2×C32 |
| Hall | C3×C5×#3862 ⋊ C2 |
| Hall | C5⋊(C7⋊D7) ⋊ C32 |
| Hall | C3×#3862 ⋊ D5 |
| Sylow | C72 ⋊ C32×D5 |
| Sylow | C5 ⋊ C3×#64425 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C5⋊#64425 |
| commutator, cosocle, hypocenter | C5×C72 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C72 | C2×C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C3 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 315 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C25⋊#64425, C3×C5×C5⋊#64425, C3×C5⋊(C5⋊#64425) |
| maximal normal subgroup of | C3×C5×C5⋊#64425 |
| maximal quotient of | C3×C25⋊#64425, C3×C5×C5⋊#64425, C3×C5⋊(C5⋊#64425) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 87);