Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×D4⋊C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ #9642 |
698 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=f,b^2=dfg,c^2=eg,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,c^b=cg,i^c=i^702024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 68360);