Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C47 · Schur multiplier (H2) = C2 |
| direct product | C47×#1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C47 | D4 |
| commutator | C4 | C2×C16×C47 |
| Frattini, cosocle | C2×C16 | C22×C47 |
| socle | C2×C47 | C22⋊C16 |
| prime radical | #41×C47 | C8 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C47 ◁ C2×C16×C47 ◁ G | |
72 conjugacy classes of subgroups.
2632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×#1401, C47×#13558, C47×#13647, … |
| maximal normal subgroup of | C2×C47×#1401, C47×#13558, C47×#13647, … |
| maximal quotient of | C47×#7335, C47×#7363, C47×D4⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 133);