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 ⋊ #1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | C22⋊D47 |
| commutator | C4×C47 | C2×C16 |
| Frattini | C2×C16 | C2×D47 |
| Fitting | C47×M64 | C2 |
| socle | C2×C47 | C22⋊C16 |
| hypercenter | M64 | D47 |
| hypocenter | C47 | #1401 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ M64 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^46,c^b=cg,d^b=dg,h^b=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1401, C2×#20241531, #26136487, … |
| maximal normal subgroup of | D47×#1401, C2×#20241531, #26136487, … |
| maximal quotient of | #26103618, #26103678, #26103715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2653);