Finite Group DatabasebetaFinite Group Databasebeta| order | 7024 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D439)⋊C4 |
| Fitting | C2×C4×C439 ⋊ C2 |
| Sylow | C439 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D439 |
| commutator | C2×C439 | C2×C4 |
| Fitting | C2×C4×C439 | C2 |
| socle | C22×C439 | C22 |
| hypercenter | C2×C4 | D439 |
| hypocenter | C439 | C22⋊C4 |
| LCS | G ▷ C2×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,439|a^2=d,b^a=bc,e^b=e^4381762 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D439, C2×(C2×D439)⋊C4, #28380700, … |
| maximal normal subgroup of | C22⋊C4×D439, C2×(C2×D439)⋊C4, #28380700, … |
| maximal quotient of | C439⋊#95, (C2×D439)⋊C8, #28380657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7024, 17);