Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊D105 |
| unambiguous semidirect product | C3⋊(C7×D105) |
| unambiguous semidirect product | C5⋊(C7×C3⋊D21) |
| unambiguous semidirect product | C7⋊(C7×C3⋊D15) |
| Fitting, socle, Hall | C32×C5×C72 ⋊ C2 |
| derived | C32×C5×C7 ⋊ C2×C7 |
| Hall | C32×C72 ⋊ D5 |
| Hall | C5×C72 ⋊ C3⋊D3 |
| Sylow | C72 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ C7×D7 |
| Sylow | C32 ⋊ C7×D35 |
| Sylow | C5 ⋊ C7×C3⋊D21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D105 |
| commutator, cosocle, hypocenter | C32×C5×C7 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C72 | C2 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 ◁ C7 | |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 630 |
1113 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C3⋊D525, C5×C7×C3⋊D105, C7×C3⋊(C3⋊(C5⋊D35)) |
| maximal normal subgroup of | C5×C7×C3⋊D105 |
| maximal quotient of | C7×C3⋊D525, C5×C7×C3⋊D105, C7×C3⋊(C3⋊(C5⋊D35)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 135);