Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C73×#2784 ⋊ C2 |
| Sylow | C73 ⋊ #36747 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D73 |
| commutator, socle, cosocle | C23×C73 | C25 |
| Fitting | C73×#2784 | C2 |
| prime radical | C22×D4×D73 | C22 |
| hypercenter | #2784 | D73 |
| hypocenter | C73 | #36747 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ #2784 | |
2146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4672 |
Polycyclic presentation:
2^8,73|a^2=g,c^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,c^b=ch,d^b=dfh,i^b=i^72,i^c=i^72,i^d=i^72,i^e=i^721204 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 377169);