Finite Group DatabasebetaFinite Group Databasebeta| order | 7630 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D109 |
| unambiguous semidirect product | C109⋊(C2×C5×C7) |
| Fitting, socle, Hall | C5×C7×C109 ⋊ C2 |
| derived, Sylow | C109 ⋊ C2×C5×C7 |
| Hall | C7×C109 ⋊ C2×C5 |
| Hall | C5×C109 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D109 |
| commutator, hypocenter | C109 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C109 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C5×C7 | |
16 conjugacy classes of subgroups.
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×#89137, C5×C7⋊#89137, C5×D7×D109, … |
| maximal normal subgroup of | C5×C7×#89137, C5×C7⋊#89137, C5×D7×D109, … |
| maximal quotient of | C5×C7×Dic109, C2×C5×C7×D109, C3×C5×C7×D109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7630, 2);