Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1828 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #15688986 |
| commutator | C23×C47 | C22×C4 |
| Frattini | C24 | C22×D47 |
| Fitting | C47×#518 | C2 |
| socle | C2×C47 | #381 |
| hypercenter | #518 | D47 |
| hypocenter | C47 | #1828 |
| LCS | G ▷ C23×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #518 | |
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,c^2=d,b^a=bd,c^a=ce,d^a=dg,h^a=h^46,f^b=fg,e^c=eg811 conjugacy classes — view the full character table.
| maximal subgroup of | #26131895, #26131896, #26131900, … |
| maximal normal subgroup of | #26131895, #26131896, #26131900, … |
| maximal quotient of | #26109737, #26109740, #26109743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4618);