Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22⋊Q8×C101 ⋊ C2 |
| Sylow | C101 ⋊ #536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D101 |
| commutator, socle | C22×C101 | C24 |
| Fitting | C22⋊Q8×C101 | C2 |
| hypercenter | C22⋊Q8 | D101 |
| hypocenter | C101 | #536 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,101|b^2=e,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^100,g^d=g^100722 conjugacy classes — view the full character table.
| maximal subgroup of | #27180404, #27180406, #27180422, … |
| maximal normal subgroup of | #27180404, #27180406, #27180422, … |
| maximal quotient of | #27173715, #27173721, #27173754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1122);