Finite Group DatabasebetaFinite Group Databasebeta| order | 6544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#13109888 |
| unambiguous semidirect product | (C2×#13109888)⋊C2 |
| Fitting | C22×C409 ⋊ C4 |
| Sylow | C409 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#13109888 |
| commutator, socle | C2×C409 | C2×C4 |
| Fitting | C22×C409 | C4 |
| hypercenter | C22 | #13109888 |
| hypocenter | C409 | C22⋊C4 |
| LCS | G ▷ C2×C409 ▷ C409 | |
| UCS | C1 ◁ C2 ◁ C22 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,409|a^2=d,b^a=bc,e^a=e^143,e^d=e^408418 conjugacy classes — view the full character table.
| maximal subgroup of | #27189775, #27189776, C2×C22⋊#13109888, … |
| maximal normal subgroup of | #27189775, #27189776, C2×C22⋊#13109888, … |
| maximal quotient of | (C2×#13109888)⋊C4, C22⋊#15692550, #27189774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6544, 45);