Finite Group DatabasebetaFinite Group Databasebeta| order | 14048 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#20296328 |
| Fitting | C2×D4×C439 ⋊ C2 |
| Sylow | C439 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D439 |
| commutator, cosocle | C2×C439 | C24 |
| Frattini | C2 | C23×D439 |
| Fitting | C2×D4×C439 | C2 |
| socle | C22×C439 | C23 |
| hypercenter | C2×D4 | D439 |
| hypocenter | C439 | C2×#41 |
| LCS | G ▷ C2×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7024 |
2210 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #43243576, #43243585, #43243597, … |
| maximal normal subgroup of | #43243576, #43243585, #43243597, … |
| maximal quotient of | C2×#28380699, C2×#28380701, C2×(C22⋊D439)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14048, 188);