Finite Group DatabasebetaFinite Group Databasebeta| order | 6132 |
| isoclinism | isoclinic class of AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×ΓL(1,𝔽8)⋊C4 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C4×C73) |
| unambiguous semidirect product | Dic7⋊(C3×C73) |
| derived, Sylow | C7 ⋊ C3×C4×C73 |
| Hall | Dic7×C73 ⋊ C3 |
| Hall | ΓL(1,𝔽8)×C73 ⋊ C4 |
| Hall | C7×C73 ⋊ C3×C4 |
| Hall | Dic7 ⋊ C3×C73 |
| Hall | ΓL(1,𝔽8) ⋊ C4×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C73 | AGL(1,𝔽7) |
| commutator, hypocenter | C7 | C3×C4×C73 |
| Frattini | C2 | AGL(1,𝔽7)×C73 |
| Fitting, socle | C2×C7×C73 | C2×C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C73 | |
24 conjugacy classes of subgroups.
1022 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6132, 18);