Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C47×D32 ⋊ C2 |
| Sylow | C47 ⋊ D64 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15688958 |
| commutator | C32×C47 | C22 |
| Frattini | C32 | C2×D47 |
| Fitting | C47×D32 | C2 |
| socle | C2×C47 | D32 |
| hypercenter | D32 | D47 |
| hypocenter | C47 | D64 |
| LCS | G ▷ C32×C47 ▷ C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 ◁ D32 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^46472 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D64, C2×#20241600, #26137330, … |
| maximal normal subgroup of | D47×D64, C2×#20241600, #26137330, … |
| maximal quotient of | #26104155, #26104156, #26104177, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2722);