Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C101 ⋊ C2 |
| Sylow | C101 ⋊ #349 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13108051 |
| commutator | C22×C101 | C2×C8 |
| Frattini | C2×C8 | C2×D101 |
| Fitting | M32×C101 | C2 |
| socle | C2×C101 | C22⋊C8 |
| hypercenter | M32 | D101 |
| hypocenter | C101 | #349 |
| LCS | G ▷ C22×C101 ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C4 ◁ C2×C8 ◁ M32 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,101|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^1001022 conjugacy classes — view the full character table.
| maximal subgroup of | #349×D101, C2×#20264958, #27172751, … |
| maximal normal subgroup of | #349×D101, C2×#20264958, #27172751, … |
| maximal quotient of | #27169055, #27169071, #27169089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 330);