Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11717581 |
| Sylow | C101 ⋊ C2×C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#87938 |
| commutator | C2×C101 | C22×C8 |
| Frattini | C22 | C22×#87938 |
| Fitting | C24×C101 | C4 |
| socle | C23×C101 | C2×C4 |
| hypercenter | C24 | #87938 |
| hypocenter | C101 | C2×C22⋊C8 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C24 | |
202 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #27185970, #27185975, C2×#20266020, … |
| maximal normal subgroup of | #27185970, #27185975, C2×#20266020, … |
| maximal quotient of | C2×#20266020, C2×#20266022, #27186363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1516);