Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C101 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #87938 |
| commutator, hypocenter | C101 | C4×C16 |
| Frattini | C2×C4 | C2×#87938 |
| Fitting | C2×C8×C101 | C4 |
| socle | C22×C101 | C2×C8 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C2×C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=c,b^2=d,c^2=e,e^2=f,g^a=g^10,g^b=g^100,g^c=g^100464 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#11717581, #27186043, #11717581⋊C16, … |
| maximal normal subgroup of | C16×#11717581, #27186043, #11717581⋊C16, … |
| maximal quotient of | C8×#13108077, #27186047, #27186171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1435);