Finite Group DatabasebetaFinite Group Databasebeta| order | 8174 |
| isoclinism | isoclinic class of D61 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×D61 |
| unambiguous semidirect product | C61⋊(C2×C67) |
| Fitting, socle, Hall | C61×C67 ⋊ C2 |
| derived, Sylow | C61 ⋊ C2×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | D61 |
| commutator, hypocenter | C61 | C2×C67 |
| Frattini | C1 | G |
| Fitting, socle | C61×C67 | C2 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C67 | |
8 conjugacy classes of subgroups.
2144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C67×#6923, C67⋊#6923, D61×D67, … |
| maximal normal subgroup of | C67×#6923, C67⋊#6923, D61×D67, … |
| maximal quotient of | C67×Dic61, C2×C67×D61, C3×C67×D61, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8174, 1);