Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#2069 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C22×D4×C47 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G | |
216 conjugacy classes of subgroups.
1081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×#2069, C47×#23622, C47×#24808, … |
| maximal normal subgroup of | C2×C47×#2069, C47×#23622, C47×#24808, … |
| maximal quotient of | C47×#10603, C47×#10605, C47×#10607, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 801);