Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×M128 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C53 | C22 |
| commutator | C2 | C2×C32×C53 |
| Frattini, cosocle | C32 | C22×C53 |
| socle | C2×C53 | C2×C32 |
| prime radical | C22×C53 | C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ G | |
38 conjugacy classes of subgroups.
4240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7511, C53×#7513, C53×#7514, … |
| maximal normal subgroup of | C53×#7511, C53×#7513, C53×#7514, … |
| maximal quotient of | C53×#7510, C53×C22⋊C64, C53×C4⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 160);