Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#1425 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | D16 |
| commutator | C16 | C2×C4×C53 |
| Frattini, cosocle | C2×C16 | C22×C53 |
| socle | C2×C53 | #366 |
| prime radical | C22×C53 | Q32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C2×C4×C53 ◁ C2×C8×C53 ◁ C2×C16×C53 ◁ G | |
50 conjugacy classes of subgroups.
2014 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7539, C53×#7541, C53×#7542, … |
| maximal normal subgroup of | C53×#7539, C53×#7541, C53×#7542, … |
| maximal quotient of | C53×#7460, C53×#7461, C53×#7472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 157);