Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #103×C101 ⋊ C2 |
| Sylow | C101 ⋊ #440 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^100,d^b=df,g^b=g^100,g^c=g^100722 conjugacy classes — view the full character table.
| maximal subgroup of | #440×D101, C2×#20265280, #27179928, … |
| maximal normal subgroup of | #440×D101, C2×#20265280, #27179928, … |
| maximal quotient of | #27169947, #27169992, #27170007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 652);