Finite Group DatabasebetaFinite Group Databasebeta| order | 14464 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×#14268655 |
| derived, Sylow | C113 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #90673 |
| commutator, hypocenter | C113 | C24×C8 |
| Frattini | C2 | C24×#90673 |
| Fitting | C23×C4×C113 | C4 |
| socle | C24×C113 | C2×C4 |
| prime radical | C24×D113 | C4 |
| cosocle | Dic113 | C25 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C23×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7232 |
1024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14464, 21494);