Finite Group DatabasebetaFinite Group Databasebeta| order | 7906 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C59 · Schur multiplier (H2) = C1 |
| direct product | C59×D67 |
| unambiguous semidirect product | C67⋊(C2×C59) |
| Fitting, socle, Hall | C59×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C59 | D67 |
| commutator, hypocenter | C67 | C2×C59 |
| Frattini | C1 | G |
| Fitting, socle | C59×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C59 | |
8 conjugacy classes of subgroups.
2065 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×D67, C2×C59×D67, C3×C59×D67, … |
| maximal normal subgroup of | D59×D67, C2×C59×D67, C3×C59×D67, … |
| maximal quotient of | C59×Dic67, C2×C59×D67, C3×C59×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7906, 2);