Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D101⋊C8 |
| derived, Sylow | C101 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #87938 |
| commutator, hypocenter | C101 | C2×C4×C8 |
| Frattini | C22 | C22×#87938 |
| Fitting | C42×C101 | C4 |
| socle | C22×C101 | C22×C4 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C42 | |
162 conjugacy classes of subgroups.
464 conjugacy classes — view the full character table.
| maximal subgroup of | #27185961, #27185963, #27185966, … |
| maximal normal subgroup of | #27185961, #27185963, #27185966, … |
| maximal quotient of | C8×D101⋊C8, #27186326, #27186330, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1505);