Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#446×C71 ⋊ C2 |
| Sylow | C71 ⋊ #22549 |
1118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9088 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=e,c^2=eh,d^2=eh,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^70,c^b=ch,d^b=de,f^c=fh,i^c=i^702018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 186456);