Finite Group DatabasebetaFinite Group Databasebeta| order | 7434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C59⋊(D7⋊C9) |
| unambiguous semidirect product | (C7⋊C9)⋊D59 |
| unambiguous semidirect product | D413⋊C9 |
| derived, Hall | C7×C59 ⋊ C2×C9 |
| Hall | C59×C7⋊C9 ⋊ C2 |
| Hall | D413 ⋊ C9 |
| Hall | C7⋊C9 ⋊ D59 |
| Sylow | C59 ⋊ D7⋊C9 |
| Sylow | C7 ⋊ C9×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊D59 |
| commutator, hypocenter | C7×C59 | C2×C9 |
| Fitting, socle | C3×C7×C59 | C2×C3 |
| LCS | G ▷ C7×C59 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,59,3|b^3=e,c^a=c^6,d^a=d^58,c^b=c^2456 conjugacy classes — view the full character table.
| maximal subgroup of | D59×D7⋊C9, C2×C59⋊(D7⋊C9), C5×C59⋊(D7⋊C9), … |
| maximal normal subgroup of | D59×D7⋊C9, C2×C59⋊(D7⋊C9), C5×C59⋊(D7⋊C9) |
| maximal quotient of | C59⋊(Dic7⋊C9), C2×C59⋊(D7⋊C9), C5×C59⋊(D7⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7434, 12);