Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#13108083 |
| Sylow | C101 ⋊ C22×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×#87938 |
| commutator | C2×C101 | C23×C4 |
| Frattini | C2 | C23×#87938 |
| Fitting | C24×C101 | C4 |
| socle | C23×C101 | C2×C4 |
| hypercenter | C24 | #87938 |
| hypocenter | C101 | C22×M16 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C24 | |
298 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #27186795, #27186798, C2×#20266057, … |
| maximal normal subgroup of | #27186795, #27186798, C2×#20266057, … |
| maximal quotient of | C22×#15692310, C2×C4×#13108083, C22×C22⋊#11717581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1621);