Finite Group DatabasebetaFinite Group Databasebeta| order | 6416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D401 |
| Fitting | C2×C4×C401 ⋊ C2 |
| derived, Sylow | C401 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D401 |
| commutator, hypocenter | C401 | C22×C4 |
| Frattini | C2 | C22×D401 |
| Fitting | C2×C4×C401 | C2 |
| socle | C22×C401 | C22 |
| LCS | G ▷ C401 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
1616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27165649, C42×D401, C22⋊C4×D401, … |
| maximal normal subgroup of | #27165649, C42×D401, C22⋊C4×D401, … |
| maximal quotient of | C42×D401, C2×C4×Dic401, C22⋊C4×D401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6416, 32);