Finite Group DatabasebetaFinite Group Databasebeta| order | 14048 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C439⋊C8 |
| derived, Sylow | C439 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D439 |
| commutator, hypocenter | C439 | C4×C8 |
| Frattini | C2×C4 | C2×D439 |
| Fitting | C42×C439 | C2 |
| socle, prime radical | C22×C439 | C2×C4 |
| cosocle | C2×C4×C439 | C22 |
| LCS | G ▷ C439 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14048 |
3536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C439⋊C8, #43243325, #43243326, … |
| maximal normal subgroup of | C8×C439⋊C8, #43243325, #43243326, … |
| maximal quotient of | C8×C439⋊C8, #43243325, #43243359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14048, 55);