Finite Group DatabasebetaFinite Group Databasebeta| order | 8174 |
| isoclinism | isoclinic class of D67 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×D67 |
| unambiguous semidirect product | C67⋊(C2×C61) |
| Fitting, socle, Hall | C61×C67 ⋊ C2 |
| derived, Sylow | C67 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | D67 |
| commutator, hypocenter | C67 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C61×C67 | C2 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C61 | |
8 conjugacy classes of subgroups.
2135 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×D67, C2×C61×D67, C3×C61×D67, … |
| maximal normal subgroup of | D61×D67, C2×C61×D67, C3×C61×D67, … |
| maximal quotient of | C61×Dic67, C2×C61×D67, C3×C61×D67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8174, 2);