Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #1387 |
136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 73 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=d,b^2=e,c^2=fg,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^46,c^b=cg,h^b=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1387, C2×#20241498, #26131203, … |
| maximal normal subgroup of | D47×#1387, C2×#20241498, #26131203, … |
| maximal quotient of | #26103160, #26103209, #26103213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2620);