Finite Group DatabasebetaFinite Group Databasebeta| order | 19072 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C149 ⋊ C4 |
| Sylow | C149 ⋊ #1409 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2384 |
Polycyclic presentation:
2^7,149|a^2=d,b^2=g,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^105,c^b=cfg,d^b=def,e^b=eg,h^b=h^148,d^c=dfg,e^d=eg,h^d=h^1481201 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 19644);