Finite Group DatabasebetaFinite Group Databasebeta| order | 4410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C7 |
| direct product | C5×C7⋊D63 |
| unambiguous semidirect product | C7⋊(C5×D63) |
| unambiguous semidirect product | C9⋊(C5×C7⋊D7) |
| Fitting, Hall | C5×C72×C9 ⋊ C2 |
| derived, Hall | C72×C9 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ D9 |
| Sylow | C72 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ C7⋊D7 |
| Sylow | C9 ⋊ C5×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊D63 |
| commutator, cosocle, hypocenter | C72×C9 | C2×C5 |
| Frattini | C3 | C5×C3⋊(C7⋊D7) |
| Fitting | C5×C72×C9 | C2 |
| socle | C3×C5×C72 | D3 |
| LCS | G ▷ C72×C9 | |
| UCS | C1 ◁ C5 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2205 |
1110 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×C7⋊D63, C52×C7⋊D63, C5×C5⋊(C7⋊D63) |
| maximal normal subgroup of | C25×C7⋊D63, C52×C7⋊D63 |
| maximal quotient of | C25×C7⋊D63, C52×C7⋊D63, C5×C5⋊(C7⋊D63) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4410, 63);