Finite Group DatabasebetaFinite Group Databasebeta| order | 7670 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C59 · Schur multiplier (H2) = C1 |
| direct product | C5×D13×C59 |
| unambiguous semidirect product | C13⋊(C2×C5×C59) |
| Fitting, socle, Hall | C5×C13×C59 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C5×C59 |
| Hall | C13×C59 ⋊ C2×C5 |
| Hall | C5×C13 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C59 | D13 |
| commutator, hypocenter | C13 | C2×C5×C59 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C59 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C59 | |
16 conjugacy classes of subgroups.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#261×C59, C5×C59⋊#261, C5×D13×D59, … |
| maximal normal subgroup of | C5×#261×C59, C5×C59⋊#261, C5×D13×D59, … |
| maximal quotient of | C5×Dic13×C59, C2×C5×D13×C59, C3×C5×D13×C59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7670, 3);