Finite Group DatabasebetaFinite Group Databasebeta| order | 6412 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C229 · Schur multiplier (H2) = C1 |
| direct product | Dic7×C229 |
| unambiguous semidirect product | C7⋊(C4×C229) |
| derived, Sylow | C7 ⋊ C4×C229 |
| Hall | C7×C229 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C229 | D7 |
| commutator, hypocenter | C7 | C4×C229 |
| Frattini | C2 | D7×C229 |
| Fitting, socle | C2×C7×C229 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C229 | |
12 conjugacy classes of subgroups.
2290 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic7×C229, Dic21×C229, Dic7×C229⋊C3, … |
| maximal normal subgroup of | C3×Dic7×C229, Dic7×C229⋊C3, ΓL(1,𝔽8)⋊C4×C229, … |
| maximal quotient of | C3×Dic7×C229, Dic21×C229, C5×Dic7×C229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6412, 2);