Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#424 ⋊ C2 |
| Sylow | C47 ⋊ #3259 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#424 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #424 | D47 |
| hypocenter | C47 | #3259 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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|b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^46,c^b=ce,d^b=dg,f^c=fg,h^c=h^46670 conjugacy classes — view the full character table.
| maximal subgroup of | #26128752, #26128755, #26128769, … |
| maximal normal subgroup of | #26128752, #26128755, #26128769, … |
| maximal quotient of | #26226267, #26226704, #26228527, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 15949);