Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#87938 |
| commutator, socle | C2×C101 | C22×C8 |
| Fitting | M16×C101 | C4 |
| hypercenter | M16 | #87938 |
| hypocenter | C101 | #504 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,d^2=e,e^2=f,g^a=g^10,c^b=cf,g^b=g^100,g^d=g^100290 conjugacy classes — view the full character table.
| maximal subgroup of | #27187520, #27187521, #27187523, … |
| maximal normal subgroup of | #27187520, #27187521, #27187523, … |
| maximal quotient of | #27187342, #27187343, #27187363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1608);