Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C101 ⋊ C4 |
| Sylow | C101 ⋊ #342 |
142 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 36 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=d,b^2=e,b^a=bc,c^a=cf,d^b=df,g^b=g^10,g^e=g^100272 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20266054, #27186830, #99×#87938, … |
| maximal normal subgroup of | C2×#20266054, #27186830, #99×#87938, … |
| maximal quotient of | #27185969, #27185973, #27185975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1426);