Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C101 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D101 |
| commutator | C22×C101 | C22×C4 |
| Fitting | C25×C101 | C2 |
| socle | C23×C101 | C23 |
| hypercenter | C25 | D101 |
| hypocenter | C101 | #379 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=f,b^a=bd,c^a=ce,g^a=g^1001628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27169036, #27171046, #27171047, … |
| maximal normal subgroup of | #27169036, #27171046, #27171047, … |
| maximal quotient of | #27169355, #27169373, #27169403, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 405);