Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#15692330 |
| Sylow | C101 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#87938 |
| commutator | C2×C101 | C22×C8 |
| Frattini | C4 | C22×#87938 |
| Fitting | C2×C8×C101 | C4 |
| socle | C22×C101 | C2×C8 |
| hypercenter | C2×C8 | #87938 |
| hypocenter | C101 | C2×M32 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
90 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #27186172, #27186184, #27186203, … |
| maximal normal subgroup of | #27186172, #27186184, #27186203, … |
| maximal quotient of | C2×#20266066, C4×#15692330, C2×#20266072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1606);