Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D101 |
| Fitting | M32×C101 ⋊ C2 |
| Sylow | C101 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D101 |
| commutator, socle | C2×C101 | C22×C8 |
| Fitting | M32×C101 | C2 |
| hypercenter | M32 | D101 |
| hypocenter | C101 | C2×M32 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
1040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #347×D101, #27172735, #349×D101, … |
| maximal normal subgroup of | #347×D101, #27172735, #349×D101, … |
| maximal quotient of | #346×D101, M32×Dic101, #27172725, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 962);