Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#1043⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | #1043⋊(C7×ΓL(1,𝔽8)) |
| Fitting, socle, Hall | C52×C72 ⋊ C3×C4 |
| derived | C52×C7 ⋊ C3×C4×C7 |
| Hall | C72×#1043 ⋊ C3 |
| Hall | C7×C7⋊(C52⋊C3) ⋊ C4 |
| Hall | #1043 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ #1043⋊C3 |
| Sylow | C52 ⋊ C4×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #1043⋊ΓL(1,𝔽8) |
| commutator, hypocenter | C52×C7 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C72 | C3×C4 |
| prime radical | C7×(C5⋊D5)⋊ΓL(1,𝔽8) | C2 |
| cosocle | C7×C5⋊D5 | C2×C3×C7 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C7 | |
120 conjugacy classes of subgroups.
238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 534);