Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #11717581⋊C8 |
| Sylow | C101 ⋊ #322 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×#87938 |
| commutator | C2×C101 | C4×C8 |
| Fitting | C2×C8×C101 | C4 |
| socle | C22×C101 | C42 |
| hypercenter | C2×C8 | #87938 |
| hypocenter | C101 | #322 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=c,b^2=d,c^2=e,d^2=f,b^a=be,g^a=g^10,g^c=g^100440 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11717581⋊C8, #27186328, C8×#13108083, … |
| maximal normal subgroup of | C2×#11717581⋊C8, #27186328, C8×#13108083, … |
| maximal quotient of | #27185954, #11717581⋊C16, #27186050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1391);