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 | C2×C4×#41×C47 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C47 | C22 |
| commutator | C2 | C24×C4×C47 |
| Frattini, cosocle | C22 | C25×C47 |
| socle | C23×C47 | C24 |
| prime radical | C22×#41×C47 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C47 ◁ G | |
1728 conjugacy classes of subgroups.
3760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#8312, C47×#10758, C47×#10772, … |
| maximal normal subgroup of | C47×#8312, C47×#10758, C47×#10772, … |
| maximal quotient of | C2×C4×#117×C47, C2×C42×D4×C47, C2×C42×Q8×C47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2156);