Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| isoclinism | isoclinic class of D91 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D91 |
| unambiguous semidirect product | C7⋊(C5×C7×D13) |
| unambiguous semidirect product | C13⋊(C5×C7×D7) |
| Fitting, socle, Hall | C5×C72×C13 ⋊ C2 |
| derived | C7×C13 ⋊ C2×C5×C7 |
| Hall | C72×C13 ⋊ C2×C5 |
| Hall | C5×C72 ⋊ D13 |
| Hall | C5×C13 ⋊ C7×D7 |
| Sylow | C72 ⋊ C5×D13 |
| Sylow | C13 ⋊ C5×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D91 |
| commutator, hypocenter | C7×C13 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C5×C7 | |
44 conjugacy classes of subgroups.
1645 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D7×D13, C5×D7×D91, C5×(C7⋊D7)⋊D13, … |
| maximal normal subgroup of | C5×C7×D7×D13, C5×D7×D91, C5×(C7⋊D7)⋊D13, … |
| maximal quotient of | C5×C7×Dic91, C2×C5×C7×D91, C5×C7×D273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 12);