Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#106×C47 ⋊ C2 |
| Sylow | C47 ⋊ #2092 |
274 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 83 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=de,d^2=g,e^2=g,b^a=bd,c^a=ce,h^a=h^46,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg,h^c=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2092, C2×#20244910, #26246072, … |
| maximal normal subgroup of | D47×#2092, C2×#20244910, #26246072, … |
| maximal quotient of | #26121250, #26121286, #26121318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6032);