Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#13108077 |
| Sylow | C101 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#87938 |
| commutator | C2×C101 | C2×C16 |
| Fitting | C42×C101 | C4 |
| socle | C22×C101 | C2×C8 |
| hypercenter | C42 | #87938 |
| hypocenter | C101 | C4⋊C16 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^10,g^d=g^100440 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#13108077, #27186083, #27186084, … |
| maximal normal subgroup of | D4⋊#13108077, #27186083, #27186084, … |
| maximal quotient of | #27186154, #27186161, #27186170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1469);