Finite Group DatabasebetaFinite Group Databasebeta| order | 18688 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C22×#120×C73 ⋊ C2 |
| Sylow | C73 ⋊ #62817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D73 |
| commutator, socle, cosocle | C22×C73 | C26 |
| Fitting | C22×#120×C73 | C2 |
| hypercenter | C22×#120 | D73 |
| hypocenter | C73 | #62817 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×#120 | |
9494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^8,73|b^a=bg,c^a=ch,d^a=dg,f^a=fh,c^b=cg,e^b=eh,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, 1078186);