Finite Group DatabasebetaFinite Group Databasebeta| order | 8684 |
| automorphism | Aut(G) order 8649264 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4342 |
| direct product | C2×D2171 |
| unambiguous semidirect product | (C2×C13)⋊D167 |
| unambiguous semidirect product | (C2×C167)⋊D13 |
| Fitting, socle | C2×C13×C167 ⋊ C2 |
| derived, Hall | C13×C167 ⋊ C22 |
| Sylow | C167 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2171 |
| commutator, hypocenter | C13×C167 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C13×C167 | C2 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
2174 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×(C13⋊C3)⋊D167, D3×D2171, C2×C3×D2171, … |
| maximal normal subgroup of | C2×(C13⋊C3)⋊D167, C2×C3×D2171, D8684 |
| maximal quotient of | D3×D2171, C2×C3×D2171, C2×D6513, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8684, 9);