Finite Group DatabasebetaFinite Group Databasebeta| order | 15666 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D373 |
| Fitting, socle, derived, Hall | C7×C373 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×C373 ⋊ C2 |
| Hall | D2611 ⋊ C3 |
| Sylow | C373 ⋊ AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D373 |
| Sylow | C7 ⋊ C3×D373 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C373 | C2×C3 |
| LCS | G ▷ C7×C373 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2611 |
Polycyclic presentation:
2,3,7,373|c^a=c^6,d^a=d^372,c^b=c^2937 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D373, C2×ΓL(1,𝔽8)⋊D373 |
| maximal normal subgroup of | AGL(1,𝔽7)×D373, C2×ΓL(1,𝔽8)⋊D373 |
| maximal quotient of | ΓL(1,𝔽8)⋊Dic373, C2×ΓL(1,𝔽8)⋊D373 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15666, 22);