Finite Group DatabasebetaFinite Group Databasebeta| order | 8684 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×D167 |
| unambiguous semidirect product | C167⋊(C22×C13) |
| unambiguous semidirect product | (C2×C167)⋊(C2×C13) |
| Fitting, socle | C2×C13×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C22×C13 |
| Hall | C13×C167 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D167 |
| commutator, hypocenter | C167 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C167 | C2 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C2×C13 | |
20 conjugacy classes of subgroups.
2210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C13⋊C3×D167, D3×C13×D167, C2×C3×C13×D167, … |
| maximal normal subgroup of | C2×C13⋊C3×D167, C2×C3×C13×D167 |
| maximal quotient of | D3×C13×D167, C2×C3×C13×D167, C2×C13×D501 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8684, 11);