Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C101 ⋊ C2 |
| Sylow | C101 ⋊ #577 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,101|a^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^100,e^b=ef,d^c=df872 conjugacy classes — view the full character table.
| maximal subgroup of | #27182893, #27182896, #27182905, … |
| maximal normal subgroup of | #27182893, #27182896, #27182905, … |
| maximal quotient of | #27179658, #27179662, #27179725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1360);