Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×D16×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2263 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,h^a=h^180,d^b=de,e^b=ef,f^b=fg2006 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 6823);