Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊#6157 |
| Fitting | C22×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6157 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C22×D4×C53 | C4 |
| hypercenter | C22×D4 | #6157 |
| hypocenter | C53 | D4×C22⋊C4 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
1252 conjugacy classes of subgroups.
310 conjugacy classes — view the full character table.
| maximal subgroup of | #28304756, #28304757, #28304764, … |
| maximal normal subgroup of | #28304756, #28304757, #28304764, … |
| maximal quotient of | C22⋊C4×C22⋊#6157, C4⋊C4×C22⋊#6157, D4×(C2×#6157)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 21012);