Finite Group DatabasebetaFinite Group Databasebeta| order | 17598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D419 |
| unambiguous semidirect product | C419⋊AGL(1,𝔽7) |
| unambiguous semidirect product | D2933⋊C3 |
| Fitting, socle, derived, Hall | C7×C419 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)×C419 ⋊ C2 |
| Hall | D2933 ⋊ C3 |
| Sylow | C419 ⋊ AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D419 |
| Sylow | C7 ⋊ C3×D419 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C419 | C2×C3 |
| LCS | G ▷ C7×C419 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2933 |
Polycyclic presentation:
2,3,7,419|c^a=c^6,d^a=d^418,c^b=c^21052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽7)×D419, C2×ΓL(1,𝔽8)⋊D419 |
| maximal normal subgroup of | AGL(1,𝔽7)×D419, C2×ΓL(1,𝔽8)⋊D419 |
| maximal quotient of | ΓL(1,𝔽8)⋊Dic419, C2×ΓL(1,𝔽8)⋊D419 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17598, 12);