Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×Dic401 |
| derived, Sylow | C401 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D401 |
| commutator, hypocenter | C401 | C42 |
| Frattini | C22 | C2×D401 |
| Fitting | C2×C4×C401 | C2 |
| socle | C22×C401 | C22 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C2×C4 | |
30 conjugacy classes of subgroups.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×Dic401, #27165647, #27165663, … |
| maximal normal subgroup of | C8×Dic401, #27165647, #27165663, … |
| maximal quotient of | #27165644, C8×Dic401, C4×#15691999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 16);