Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C24 |
| direct product | C2×C53×#344 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C53 | C22⋊C4 |
| commutator | C22 | C2×C42×C53 |
| Frattini, cosocle | C22×C4 | C23×C53 |
| socle | C22×C53 | #95 |
| prime radical | C24×C53 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C53 ◁ C23×C4×C53 ◁ G | |
388 conjugacy classes of subgroups.
2332 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C53×#344, C53×#10711, C53×#10729, … |
| maximal normal subgroup of | C4×C53×#344, C53×#10711, C53×#10729, … |
| maximal quotient of | C2×C53×#1281, C53×#7918, C53×#7919, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 475);