Finite Group DatabasebetaFinite Group Databasebeta| order | 6370 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×D13 |
| unambiguous semidirect product | C13⋊(C2×C5×C72) |
| Fitting, socle, Hall | C5×C72×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C5×C72 |
| Hall | C72×C13 ⋊ C2×C5 |
| Hall | C5×C13 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C72 | D13 |
| commutator, hypocenter | C13 | C2×C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C5×C72×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C72 | |
80 conjugacy classes of subgroups.
1960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C72×#261, C5×C7×C7⋊#261, C5×C7×D7×D13, … |
| maximal normal subgroup of | C5×C72×#261, C5×C7×C7⋊#261, C5×C7×D7×D13, … |
| maximal quotient of | C5×C72×Dic13, C2×C5×C72×D13, C5×C72×D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6370, 10);