Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1765 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D47 |
| commutator | C4×C47 | C2×C42 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#416 | C2 |
| socle | C22×C47 | C4×D4 |
| hypercenter | #416 | D47 |
| hypocenter | C47 | #1765 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 ◁ #416 | |
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^46,c^b=cg,h^b=h^46,h^c=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1765, C2×#20243235, #26214120, … |
| maximal normal subgroup of | D47×#1765, C2×#20243235, #26214120, … |
| maximal quotient of | #26106957, #26106963, #26106974, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4357);