Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C23 |
| direct product | C2×C47×D32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | D16 |
| commutator, Frattini, cosocle | C16 | C23×C47 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C2×C4×C47 ◁ C2×C8×C47 ◁ C2×C16×C47 ◁ G | |
120 conjugacy classes of subgroups.
1786 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#7537, C47×#7541, C4×C47×D32, … |
| maximal normal subgroup of | C47×#7537, C47×#7541, C4×C47×D32, … |
| maximal quotient of | C2×C47×#1415, C2×C47×#1423, C4×C47×D32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 991);