Finite Group DatabasebetaFinite Group Databasebeta| order | 8684 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C167⋊#261 |
| Fitting, socle, derived, Hall | C13×C167 ⋊ C4 |
| Sylow | C167 ⋊ #261 |
| Sylow | C13 ⋊ Dic167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C167 | C4 |
| LCS | G ▷ C13×C167 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,167|a^2=b,c^a=c^5,d^a=d^166,c^b=c^12671 conjugacy classes — view the full character table.
| maximal subgroup of | C167⋊AGL(1,𝔽13), C3×C167⋊#261, C3⋊(C167⋊#261) |
| maximal normal subgroup of | C167⋊AGL(1,𝔽13), C3×C167⋊#261 |
| maximal quotient of | C3×C167⋊#261, C3⋊(C167⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8684, 7);