Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C73×#1438 ⋊ C2 |
| Sylow | C73 ⋊ #15140 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D73 |
| commutator, socle, cosocle | C24×C73 | C24 |
| Fitting | C73×#1438 | C2 |
| prime radical | C22×#14556587 | C2 |
| hypercenter | #1438 | D73 |
| hypocenter | C73 | #15140 |
| LCS | G ▷ C24×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
2854 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9344 |
Polycyclic presentation:
2^8,73|a^2=ef,b^2=f,c^2=e,d^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,i^c=i^72,i^d=i^721648 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 106262);