Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 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,b^a=bc,c^a=cf,f^a=fg,h^a=h^46,d^b=df,d^c=dg670 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1390, C2×#20241506, #26131219, … |
| maximal normal subgroup of | D47×#1390, C2×#20241506, #26131219, … |
| maximal quotient of | #26103237, #26103273, #26103276, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2628);