Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C47×M64 ⋊ C2 |
| Sylow | C47 ⋊ #1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D47)⋊C4 |
| commutator | C22×C47 | C2×C16 |
| Frattini | C2×C16 | C2×D47 |
| Fitting | C47×M64 | C2 |
| socle | C2×C47 | C22⋊C16 |
| hypercenter | M64 | D47 |
| hypocenter | C47 | #1400 |
| LCS | G ▷ C22×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ M64 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1400, C2×#20241527, #26136480, … |
| maximal normal subgroup of | D47×#1400, C2×#20241527, #26136480, … |
| maximal quotient of | #26103616, #26103676, #26103718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2649);