Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #407×D53 |
| Fitting | C53×#407 ⋊ C2 |
| Sylow | C53 ⋊ C2×#407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D53 |
| commutator, socle | C22×C53 | C23×C4 |
| Fitting | C53×#407 | C2 |
| hypercenter | #407 | D53 |
| hypocenter | C53 | C2×#407 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C2×C4 ◁ #407 | |
1008 conjugacy classes of subgroups.
784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1284, #27273814, #27273818, … |
| maximal normal subgroup of | D53×#1284, #27273814, #27273818, … |
| maximal quotient of | D53×#1462, D53×#1463, D53×#1464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 12943);