Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×Dic53 |
| derived, Sylow | C53 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | D53 |
| commutator, hypocenter | C53 | C25×C4 |
| Frattini | C2 | C25×D53 |
| Fitting, socle | C26×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C26 | |
10552 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20272937, #379×Dic53, #27315250, … |
| maximal normal subgroup of | C2×#20272937, #379×Dic53, #27315250, … |
| maximal quotient of | C24×C4×Dic53, C24×C22⋊Dic53, C24×C4⋊Dic53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19300);