Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#463 ⋊ C2 |
| Sylow | C47 ⋊ #3250 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#463 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #463 | D47 |
| hypocenter | C47 | #3250 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #463 | |
360 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|d^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^46,f^c=fg469 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#3250, C2×#20254737, #27089108, … |
| maximal normal subgroup of | D47×#3250, C2×#20254737, #27089108, … |
| maximal quotient of | #26226170, #26226171, #26226651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15859);