Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C101 ⋊ #364 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4⋊#87938 |
| commutator | C4×C101 | C2×C8 |
| Frattini | C2×C4 | C2×#87938 |
| Fitting | C42×C101 | C4 |
| socle | C2×C101 | C4⋊C8 |
| hypercenter | C42 | #87938 |
| hypocenter | C101 | #364 |
| LCS | G ▷ C4×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C42 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,b^2=c,c^2=f,d^2=e,e^2=f,b^a=bc,c^a=cf,g^a=g^10,g^b=g^100,g^d=g^100428 conjugacy classes — view the full character table.
| maximal subgroup of | #27186140, #27186141, #27186142, … |
| maximal normal subgroup of | #27186140, #27186141, #27186142, … |
| maximal quotient of | #27186155, #27186162, #27186176, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1472);