Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D101⋊C32 |
| derived, Sylow | C101 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #87938 |
| commutator, hypocenter | C101 | C2×C32 |
| Frattini | C8 | C2×#87938 |
| Fitting | C16×C101 | C4 |
| socle | C2×C101 | C2×C16 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^10,g^b=g^100,g^c=g^100464 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#87938, #27186238, #27186281, … |
| maximal normal subgroup of | C32×#87938, #27186238, #27186281, … |
| maximal quotient of | #27186237, #27186246, #27186290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1480);