Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#3126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C47 |
| prime radical | C47×#540 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ #117×C47 ◁ G | |
382 conjugacy classes of subgroups.
1504 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×#3126, C47×#60557, C47×#60566, … |
| maximal normal subgroup of | C2×C47×#3126, C47×#60557, C47×#60566, … |
| maximal quotient of | C47×#20745, C47×#21128, C47×#21131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 1858);