Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×#11744753 |
| derived, Sylow | C113 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #90673 |
| commutator, hypocenter | C113 | C42×C8 |
| Frattini | C23 | C22×#90673 |
| Fitting | C2×C42×C113 | C4 |
| socle, prime radical | C23×C113 | C22×C4 |
| cosocle | C22×Dic113 | C23 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C2×C42 | |
408 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14464 |
1024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 20162);