Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×D35 |
| unambiguous semidirect product | C5⋊(D7×C7⋊C9) |
| derived, Hall | C5×C72 ⋊ C2×C9 |
| Hall | C5×C7×C7⋊C9 ⋊ C2 |
| Hall | C7×D35 ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ D5 |
| Sylow | C72 ⋊ C9×D5 |
| Sylow | C5 ⋊ D7×C7⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D35 |
| commutator, hypocenter | C5×C72 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C72 | C2×C3 |
| prime radical | C3×C7×D35 | C3 |
| LCS | G ▷ C5×C72 | |
| UCS | C1 ◁ C3 | |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 630 |
285 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7⋊C9×D175, C5×C7⋊C9×D35, C7⋊C9×C5⋊D35 |
| maximal normal subgroup of | C5×C7⋊C9×D35 |
| maximal quotient of | C7⋊C9×D175, C5×C7⋊C9×D35, C7⋊C9×C5⋊D35 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 52);