Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#343 ⋊ C2 |
| Sylow | C47 ⋊ #1742 |
388 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,e^2=g,b^a=bd,d^a=dg,e^b=eg,h^c=h^46550 conjugacy classes — view the full character table.
| maximal subgroup of | #26126477, #26126479, #26126487, … |
| maximal normal subgroup of | #26126477, #26126479, #26126487, … |
| maximal quotient of | #26105867, #26105870, #26105879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4247);