Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#15692303 |
| Fitting | C22×Q8×C101 ⋊ C2 |
| Sylow | C101 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D101 |
| commutator | C2×C101 | C25 |
| Frattini | C2 | C24×D101 |
| Fitting | C22×Q8×C101 | C2 |
| socle | C22×C101 | C24 |
| hypercenter | C22×Q8 | D101 |
| hypocenter | C101 | C2×2−1+4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C22 ◁ C22×Q8 | |
794 conjugacy classes of subgroups.
1034 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27171090, #27171093, #27171104, … |
| maximal normal subgroup of | #27171090, #27171093, #27171104, … |
| maximal quotient of | C2×#20265653, C2×#20265655, C2×#20265658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1383);