Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C47 ⋊ #1375 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic47 |
| commutator | C4×C47 | C4×C8 |
| Frattini | C22×C8 | C2×D47 |
| Fitting | C2×M32×C47 | C2 |
| socle | C22×C47 | #97 |
| hypercenter | C2×M32 | D47 |
| hypocenter | C47 | #1375 |
| LCS | G ▷ C4×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M32 | |
140 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 77 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,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,d^b=dg,h^b=h^46964 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1375, C2×#20241467, #26131126, … |
| maximal normal subgroup of | D47×#1375, C2×#20241467, #26131126, … |
| maximal quotient of | #26103107, #26103119, #26103126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2589);