Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C149 ⋊ #2993 |
354 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9536 |
Polycyclic presentation:
2^7,149|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^105,c^b=ce,d^b=dg,h^b=h^148,h^c=h^148,h^f=h^148562 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 21456);