Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #423 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#87938 |
| commutator, socle | C22×C101 | C22×C4 |
| Fitting | C42×C101 | C4 |
| hypercenter | C42 | #87938 |
| hypocenter | C101 | #423 |
| LCS | G ▷ C22×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C42 | |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=e,b^2=d,e^2=f,b^a=bd,c^a=cf,g^a=g^10,g^c=g^100,g^e=g^100428 conjugacy classes — view the full character table.
| maximal subgroup of | #27186018, #27186024, #27186029, … |
| maximal normal subgroup of | #27186018, #27186024, #27186029, … |
| maximal quotient of | #27186687, #27186690, #27186693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1553);