Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×C8×Dic53 |
| derived, Sylow | C53 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D53 |
| commutator, hypocenter | C53 | C42×C8 |
| Frattini | C22×C4 | C22×D53 |
| Fitting | C2×C4×C8×C53 | C2 |
| socle | C23×C53 | C22×C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C4×C8 | |
408 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27270947, C82×Dic53, #322×Dic53, … |
| maximal normal subgroup of | #27270947, C82×Dic53, #322×Dic53, … |
| maximal quotient of | C82×Dic53, C4×C8×#88322, #322×Dic53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4191);