Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #461 |
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^100,e^c=ef719 conjugacy classes — view the full character table.
| maximal subgroup of | #461×D101, C2×#20265380, #27180583, … |
| maximal normal subgroup of | #461×D101, C2×#20265380, #27180583, … |
| maximal quotient of | #27170505, #27170509, #27170519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 752);