Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D401 |
| unambiguous semidirect product | C401⋊C24 |
| unambiguous semidirect product | (C2×C401)⋊C23 |
| Fitting, socle | C23×C401 ⋊ C2 |
| derived, Sylow | C401 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D401 |
| commutator, hypocenter | C401 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C401 | C2 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D401, C2×#20264343, #27165705, … |
| maximal normal subgroup of | C22⋊C4×D401, C2×#20264343, #27165705, … |
| maximal quotient of | C22×C4×D401, C23×Dic401, C2×D4×D401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 42);