Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #344 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13108051 |
| commutator | C22×C101 | C42 |
| Frattini | C22×C4 | C2×D101 |
| Fitting | #117×C101 | C2 |
| socle | C2×C101 | #95 |
| hypercenter | #117 | D101 |
| hypocenter | C101 | #344 |
| LCS | G ▷ C22×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #117 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1001022 conjugacy classes — view the full character table.
| maximal subgroup of | #344×D101, C2×#20264947, #27170933, … |
| maximal normal subgroup of | #344×D101, C2×#20264947, #27170933, … |
| maximal quotient of | #27168976, #27168980, #27168981, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 319);