Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C53 · Schur multiplier (H2) = C22 |
| direct product | C53×#1385 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C53 | #106 |
| commutator | C8 | C42×C53 |
| Frattini, cosocle | C22×C8 | C22×C53 |
| socle | C2×C53 | #340 |
| prime radical | C23×C53 | Q16 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C53 ◁ C22×C4×C53 ◁ C22×C8×C53 ◁ G | |
124 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#7424, C53×#7425, C2×C53×#1385, … |
| maximal normal subgroup of | C53×#7424, C53×#7425, C2×C53×#1385, … |
| maximal quotient of | C53×#7157, C53×#7173, C53×#7220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 117);