Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| direct product | C24×C4×D53 |
| Fitting | C24×C4×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D53 |
| commutator, hypocenter | C53 | C25×C4 |
| Frattini | C2 | C25×D53 |
| Fitting | C24×C4×C53 | C2 |
| socle | C25×C53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
1792 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×C22⋊#95, C2×#20272936, #27305297, … |
| maximal normal subgroup of | D53×C22⋊#95, C2×#20272936, #27305297, … |
| maximal quotient of | C23×C42×D53, C24×C4×Dic53, C23×C22⋊C4×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19299);