Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C149 ⋊ C4 |
| Sylow | C149 ⋊ #1892 |
380 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4768 |
Polycyclic presentation:
2^7,149|a^2=f,b^2=df,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^44,h^b=h^105,h^f=h^148562 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 20523);