Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C101 ⋊ C4 |
| Sylow | C101 ⋊ #440 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#87938 |
| commutator | C4×C101 | C22×C4 |
| Frattini | C4 | C22×#87938 |
| Fitting | SD16×C101 | C4 |
| socle | C2×C101 | C4×D4 |
| hypercenter | SD16 | #87938 |
| hypocenter | C101 | #440 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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^91,d^b=df,g^c=g^10,g^e=g^100197 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20266216, #27187886, AGL(1,ℤ/8)×#87938, … |
| maximal normal subgroup of | C2×#20266216, #27187886, AGL(1,ℤ/8)×#87938, … |
| maximal quotient of | SD16⋊#11717581, #27186722, #27186723, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1588);