Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C47 · Schur multiplier (H2) = C29 |
| direct product | C22×#131×C47 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C47 | C22 |
| commutator | C2 | C24×C4×C47 |
| Frattini, cosocle | C4 | C25×C47 |
| socle | C23×C47 | C22×C4 |
| prime radical | C22×#41×C47 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C47 ◁ G | |
1504 conjugacy classes of subgroups; only the 1384 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 1384 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
3760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#10759, C47×#10760, C47×#10764, … |
| maximal normal subgroup of | C47×#10759, C47×#10760, C47×#10764, … |
| maximal quotient of | C22×C47×#405, C2×C4×#131×C47, C22×C47×#408, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2303);