Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#95×C181 ⋊ C2 |
| Sylow | C181 ⋊ #1439 |
780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=g,b^2=d,b^a=bd,c^a=ce,h^a=h^180,c^b=cf,h^c=h^1803644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 2756);