Finite Group DatabasebetaFinite Group Databasebeta| order | 14048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C439 ⋊ C2 |
| Sylow | C439 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D439 |
| commutator, socle, cosocle | C2×C439 | C24 |
| Fitting | #41×C439 | C2 |
| hypercenter | #41 | D439 |
| hypocenter | C439 | 2−1+4 |
| LCS | G ▷ C2×C439 ▷ C439 | |
| UCS | C1 ◁ C2 ◁ #41 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7024 |
Polycyclic presentation:
2^5,439|b^2=e,c^2=e,b^a=be,d^a=de,c^b=ce,f^d=f^4382207 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43243775, #43243778, #43243785, … |
| maximal normal subgroup of | #43243775, #43243778, #43243785, … |
| maximal quotient of | #43244080, #43244081, #43244083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14048, 193);