Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊Dic53 |
| Sylow | C53 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D53 |
| commutator | C22×C53 | C23×C4 |
| Fitting | C23×D4×C53 | C2 |
| socle | C23×C53 | C24 |
| hypercenter | C23×D4 | D53 |
| hypocenter | C53 | D4×C22⋊C4 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1252 conjugacy classes of subgroups.
1090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27280509, #27280513, #27280537, … |
| maximal normal subgroup of | #27280509, #27280513, #27280537, … |
| maximal quotient of | C22⋊C4×C22⋊Dic53, C4⋊C4×C22⋊Dic53, D4×#13133124, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 7332);