Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#1422 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C53 | D4 |
| commutator | C4 | C2×C16×C53 |
| Frattini, cosocle | C2×C16 | C22×C53 |
| socle | C2×C53 | C4⋊C16 |
| prime radical | C22×C53 | M32 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C16×C53 ◁ C2×C16×C53 ◁ G | |
58 conjugacy classes of subgroups.
2968 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7381, C53×#7382, C53×#7447, … |
| maximal normal subgroup of | C53×#7381, C53×#7382, C53×#7447, … |
| maximal quotient of | C53×#7455, C53×#7458, C53×#7467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 154);