Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C181 ⋊ C2 |
| Sylow | C181 ⋊ #2994 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
Polycyclic presentation:
2^7,181|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,d^b=dg,h^b=h^180,h^c=h^180,h^d=h^1803650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 13669);