Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #13893 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D73 |
| commutator | C23×C73 | C23×C4 |
| Fitting | C73×#1434 | C2 |
| socle, prime radical, cosocle | C24×C73 | C24 |
| hypercenter | #1434 | D73 |
| hypocenter | C73 | #13893 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ #1434 | |
1298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18688 |
Polycyclic presentation:
2^8,73|a^2=h,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,d^a=de,i^a=i^72,c^b=cg,i^b=i^722092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18688, 91692);