Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #546×C181 ⋊ C2 |
| Sylow | C181 ⋊ #3264 |
568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
Polycyclic presentation:
2^7,181|e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^180,d^b=de,e^b=eg,e^d=eg,h^d=h^1802279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 15991);