Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C71×#1389 ⋊ C2 |
| Sylow | C71 ⋊ #12646 |
428 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|a^2=e,b^2=f,c^2=e,d^2=gh,e^2=h,f^2=g,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,d^b=dh,i^b=i^70,i^c=i^701184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 84832);