Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #137×C181 ⋊ C4 |
| Sylow | C181 ⋊ #2955 |
456 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^19,e^b=eg,h^b=h^180,h^c=h^162,h^f=h^180539 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 21283);