Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C47 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D47 |
| commutator, socle | C22×C47 | C22×C8 |
| Fitting | C8×Q8×C47 | C2 |
| hypercenter | C8×Q8 | D47 |
| hypocenter | C47 | #2183 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^46,h^c=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | #26128048, #26128052, #26128062, … |
| maximal normal subgroup of | #26128048, #26128052, #26128062, … |
| maximal quotient of | #26131627, #26131633, #26133895, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6419);