Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×#87938 |
| Fitting | Q16×C101 ⋊ C4 |
| Sylow | C101 ⋊ C4×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#87938 |
| commutator | C4×C101 | C22×C4 |
| Frattini | C4 | C22×#87938 |
| Fitting | Q16×C101 | C4 |
| socle | C2×C101 | C4×D4 |
| hypercenter | Q16 | #87938 |
| hypocenter | C101 | C4×Q16 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q16 | |
110 conjugacy classes of subgroups.
203 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×#87938, Q32×#87938, #27187528, … |
| maximal normal subgroup of | SD32×#87938, Q32×#87938, #27187528, … |
| maximal quotient of | Q16×#11717581, #27186719, #27186720, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1587);