Finite Group DatabasebetaFinite Group Databasebeta| order | 14048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C439 ⋊ C2 |
| Sylow | C439 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D439 |
| commutator, socle, cosocle | C22×C439 | C23 |
| Fitting | C4⋊C4×C439 | C2 |
| prime radical | C22×D439 | C22 |
| hypercenter | C4⋊C4 | D439 |
| hypocenter | C439 | C22⋊Q8 |
| LCS | G ▷ C22×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7024 |
Polycyclic presentation:
2^5,439|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=f^438,f^c=f^4382204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43243756, #43243761, #43243767, … |
| maximal normal subgroup of | #43243756, #43243761, #43243767, … |
| maximal quotient of | #43243461, #43243478, #43243489, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14048, 126);