Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic401 |
| derived, Sylow | C401 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D401 |
| commutator, hypocenter | C401 | C22×C4 |
| Frattini | C2 | C22×D401 |
| Fitting, socle | C23×C401 | C2 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27165644, C2×C4×Dic401, C2×#20264343, … |
| maximal normal subgroup of | #27165644, C2×C4×Dic401, C2×#20264343, … |
| maximal quotient of | C2×C4×Dic401, C2×C22⋊Dic401, C2×C4⋊Dic401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 33);