Finite Group DatabasebetaFinite Group Databasebeta| order | 6464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×C22⋊#87938 |
| unambiguous semidirect product | D101⋊(C2×C22⋊C4) |
| unambiguous semidirect product | (C2×#87938)⋊C23 |
| Fitting | C24×C101 ⋊ C4 |
| Sylow | C101 ⋊ C22×C22⋊C4 |
| 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×C22⋊C4 |
| LCS | G ▷ C2×C101 ▷ C101 | |
| UCS | C1 ◁ C23 ◁ C24 | |
674 conjugacy classes of subgroups.
440 conjugacy classes — view the full character table.
| maximal subgroup of | #27186305, #27186306, #27186313, … |
| maximal normal subgroup of | #27186305, #27186306, #27186313, … |
| maximal quotient of | C22×(C2×#87938)⋊C4, C2×C4×C22⋊#87938, C2×#20266118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6464, 1610);