Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#15692309 |
| Fitting | C2×C8×C101 ⋊ C4 |
| Sylow | C101 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#87938 |
| commutator | C2×C101 | C2×C42 |
| Frattini | C4 | C22×#87938 |
| Fitting | C2×C8×C101 | C4 |
| socle | C22×C101 | C42 |
| hypercenter | C2×C8 | #87938 |
| hypocenter | C101 | C2×#97 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C8 | |
146 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #27186172, #27186178, #97×#87938, … |
| maximal normal subgroup of | #27186172, #27186178, #97×#87938, … |
| maximal quotient of | C2×#20266018, #27186326, C2×#11717581⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1506);