Finite Group DatabasebetaFinite Group Databasebeta| order | 6396 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×Dic123 |
| unambiguous semidirect product | C3⋊(C13×Dic41) |
| derived, Hall | C3×C41 ⋊ C4×C13 |
| Hall | C3×C13×C41 ⋊ C4 |
| Hall | C13×C41 ⋊ Dic3 |
| Sylow | C41 ⋊ Dic3×C13 |
| Hall | C3×C13 ⋊ Dic41 |
| Sylow | C3 ⋊ C13×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C13 | D123 |
| commutator, hypocenter | C3×C41 | C4×C13 |
| Frattini | C2 | C13×D123 |
| Fitting, socle | C2×C3×C13×C41 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C2×C13 | |
24 conjugacy classes of subgroups.
1638 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×Dic369, C13⋊C3×Dic123, C3×C13×Dic123, … |
| maximal normal subgroup of | C13⋊C3×Dic123, C3×C13×Dic123, C5×C13×Dic123, … |
| maximal quotient of | C13×Dic369, C3×C13×Dic123, C13×C3⋊Dic123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6396, 7);