Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×#388×C71 ⋊ C2 |
| Sylow | C71 ⋊ #36796 |
1714 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=g,c^2=f,d^2=g,b^a=bf,c^a=cg,d^a=df,e^a=efh,i^a=i^70,c^b=ch,d^b=dfh2012 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 378523);