Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C73 ⋊ #13812 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D73 |
| commutator | C22×C73 | C22×C42 |
| Fitting | C4×#95×C73 | C2 |
| socle, prime radical, cosocle | C24×C73 | C24 |
| hypercenter | C4×#95 | D73 |
| hypocenter | C73 | #13812 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C4×#95 | |
1546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=g,b^2=h,c^2=ef,d^2=fg,b^a=be,c^a=cf,i^a=i^72,d^b=de2980 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 91059);