Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C16×Dic53 |
| derived, Sylow | C53 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D53 |
| commutator, hypocenter | C53 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D53 |
| Fitting | C22×C16×C53 | C2 |
| socle | C23×C53 | C2×C8 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C16 | |
216 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271778, #27271782, C4×C16×Dic53, … |
| maximal normal subgroup of | #27271778, #27271782, C4×C16×Dic53, … |
| maximal quotient of | C2×C16×#88322, C2×#20272634, C16×#11719917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6096);