Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C221 |
| direct product | C26×D47 |
| unambiguous semidirect product | C47⋊C27 |
| unambiguous semidirect product | (C2×C47)⋊C26 |
| Fitting, socle | C26×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D47 |
| commutator, hypocenter | C47 | C27 |
| Frattini | C1 | G |
| Fitting, socle | C26×C47 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C26 | |
58424 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26147433, C2×#379×D47, C22×#15688978, … |
| maximal normal subgroup of | #26147433, C2×#379×D47, C22×#15688978, … |
| maximal quotient of | C25×C4×D47, C26×Dic47, C24×D4×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19324);