Finite Group DatabasebetaFinite Group Databasebeta| order | 14048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C439 ⋊ C2 |
| Sylow | C439 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D439 |
| commutator, socle, cosocle | C22×C439 | C23 |
| Fitting | C22⋊C4×C439 | C2 |
| hypercenter | C22⋊C4 | D439 |
| hypocenter | C439 | #121 |
| LCS | G ▷ C22×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7024 |
Polycyclic presentation:
2^5,439|b^2=d,b^a=bd,c^a=ce,f^b=f^438,f^c=f^4382204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #121×D439, C2×#28380716, #43244112, … |
| maximal normal subgroup of | #121×D439, C2×#28380716, #43244112, … |
| maximal quotient of | #43243463, #43243480, #43243482, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14048, 119);