Finite Group DatabasebetaFinite Group Databasebeta| order | 17682 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D421 |
| Fitting, socle, derived, Hall | C7×C421 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×C421 ⋊ C2 |
| Hall | D2947 ⋊ C3 |
| Sylow | C421 ⋊ AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D421 |
| Sylow | C7 ⋊ C3×D421 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C421 | C2×C3 |
| LCS | G ▷ C7×C421 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2947 |
Polycyclic presentation:
2,3,7,421|c^a=c^6,d^a=d^420,c^b=c^21057 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×D421, C2×ΓL(1,𝔽8)⋊D421 |
| maximal normal subgroup of | AGL(1,𝔽7)×D421, C2×ΓL(1,𝔽8)⋊D421 |
| maximal quotient of | ΓL(1,𝔽8)⋊Dic421, C2×ΓL(1,𝔽8)⋊D421 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17682, 27);