Finite Group DatabasebetaFinite Group Databasebeta| order | 6396 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic533⋊C3 |
| derived, Hall | C13×C41 ⋊ C3×C4 |
| Hall | Dic533 ⋊ C3 |
| Hall | C13⋊C3×C41 ⋊ C4 |
| Sylow | C41 ⋊ Dic13⋊C3 |
| Hall | C13⋊C3 ⋊ Dic41 |
| Sylow | C13 ⋊ C3×Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C13⋊C3)⋊D41 |
| commutator, hypocenter | C13×C41 | C3×C4 |
| Fitting, socle | C2×C13×C41 | C2×C3 |
| LCS | G ▷ C13×C41 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,13,41,2|a^2=e,c^a=c^12,d^a=d^40,c^b=c^3296 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic533⋊C3, C3⋊(Dic533⋊C3), C5×Dic533⋊C3, … |
| maximal normal subgroup of | C3×Dic533⋊C3, C5×Dic533⋊C3, (Dic533⋊C3)⋊C5 |
| maximal quotient of | Dic533⋊C9, C3×Dic533⋊C3, C3⋊(Dic533⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6396, 12);