Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #2110 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C4×Dic47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C2×C8 | C22×D47 |
| Fitting | C2×M32×C47 | C2 |
| socle | C2×C47 | C2×#97 |
| hypercenter | C2×M32 | D47 |
| hypocenter | C47 | #2110 |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ C2×M32 | |
160 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,c^b=cg,d^b=dg,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | #26131110, #26131112, #26131299, … |
| maximal normal subgroup of | #26131110, #26131112, #26131299, … |
| maximal quotient of | #26125282, #26125284, #26125286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6114);