Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#14270406 |
| unambiguous semidirect product | D461⋊(C22×C4) |
| Fitting, socle | C23×C461 ⋊ C4 |
| derived, Sylow | C461 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #14270406 |
| commutator, hypocenter | C461 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C461 | C4 |
| prime radical | C23×D461 | C2 |
| cosocle | D461 | C24 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3688 |
952 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 235);