Finite Group DatabasebetaFinite Group Databasebeta| order | 14752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D461⋊C16 |
| derived, Sylow | C461 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14270406 |
| commutator, hypocenter | C461 | C2×C16 |
| Frattini | C4 | C2×#14270406 |
| Fitting | C8×C461 | C4 |
| socle | C2×C461 | C2×C8 |
| prime radical | C2×D461 | C8 |
| cosocle | #16814779 | C22 |
| LCS | G ▷ C461 | |
| UCS | C1 ◁ C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7376 |
Polycyclic presentation:
2^5,461|a^2=c,c^2=d,d^2=e,f^a=f^48,f^b=f^460,f^c=f^460952 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#14270406, #44442963, #44442988, … |
| maximal normal subgroup of | C16×#14270406, #44442963, #44442988, … |
| maximal quotient of | #44442962, #44442971, #44442997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14752, 219);