Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C4×#117×C71 ⋊ C2 |
| Sylow | C71 ⋊ #21421 |
1222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4544 |
Polycyclic presentation:
2^8,71|a^2=g,b^2=eg,c^2=h,d^2=f,b^a=be,c^a=cf,e^a=eh,i^a=i^70,e^b=eh,g^b=gh2864 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 174918);