Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C53 · Schur multiplier (H2) = C2×C4 |
| direct product | C53×#1655 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C53 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ C42×C53 ◁ G | |
262 conjugacy classes of subgroups.
1060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C53×#13677, C2×C53×#1655, C53×#18984, … |
| maximal normal subgroup of | C53×#13677, C2×C53×#1655, C53×#18984, … |
| maximal quotient of | C53×#7734, C53×#7742, C53×#7745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 387);