Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C47×#540 ⋊ C2 |
| Sylow | C47 ⋊ #3221 |
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^46532 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#3221, C2×#20254443, #27087681, … |
| maximal normal subgroup of | D47×#3221, C2×#20254443, #27087681, … |
| maximal quotient of | #26225657, #26226064, #26226861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15565);