Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C64 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #64408⋊C64 |
| derived, Sylow | C73 ⋊ C4×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10596842 |
| commutator, hypocenter | C73 | C4×C64 |
| Frattini | C16 | C2×#10596842 |
| Fitting | C32×C73 | C8 |
| socle | C2×C73 | C4×C32 |
| prime radical | C2×D73 | C2×C32 |
| cosocle | #17989518 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C32 | |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,i^a=i^10,i^b=i^46,i^c=i^27,i^d=i^72,i^e=i^72544 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 1116731);