Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ #1762 |
388 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=e,b^2=f,c^2=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^46,c^b=cg,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | #26108161, #26108163, #26108175, … |
| maximal normal subgroup of | #26108161, #26108163, #26108175, … |
| maximal quotient of | #26106883, #26106893, #26106928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4338);