Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×#1398 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C53 | C42 |
| commutator | C4 | C4×C8×C53 |
| Frattini, cosocle | C2×C16 | C22×C53 |
| socle | C2×C53 | #346 |
| prime radical | C22×C53 | M32 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C8×C53 ◁ G | |
60 conjugacy classes of subgroups.
2332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7333, C53×#7389, C53×#7390, … |
| maximal normal subgroup of | C53×#7333, C53×#7389, C53×#7390, … |
| maximal quotient of | C53×#7330, C53×#7332, C53×#7466, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 130);