Finite Group DatabasebetaFinite Group Databasebeta| order | 6544 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#13109888 |
| Fitting | C4×C409 ⋊ C4 |
| derived, Sylow | C409 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #13109888 |
| commutator, hypocenter | C409 | C42 |
| Frattini | C2 | C2×#13109888 |
| Fitting | C4×C409 | C4 |
| socle | C2×C409 | C2×C4 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
424 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#13109888, #27189771, #27189781, … |
| maximal normal subgroup of | C8×#13109888, #27189771, #27189781, … |
| maximal quotient of | (C2×#13109888)⋊C4, C8×#13109888, C4×#15692550, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6544, 44);