Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C47×#416 ⋊ C2 |
| Sylow | C47 ⋊ #2053 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13094010 |
| commutator | C22×C4×C47 | C23 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#416 | C2 |
| socle | C2×C47 | #394 |
| hypercenter | #416 | D47 |
| hypocenter | C47 | #2053 |
| LCS | G ▷ C22×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #416 | |
264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,f^b=fg,h^b=h^46670 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#2053, C2×#20244692, #26244197, … |
| maximal normal subgroup of | D47×#2053, C2×#20244692, #26244197, … |
| maximal quotient of | #26120010, #26120012, #26120017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5814);