Finite Group DatabasebetaFinite Group Databasebeta| order | 5406 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C17×D53 |
| unambiguous semidirect product | C53⋊(C2×C3×C17) |
| Fitting, socle, Hall | C3×C17×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C3×C17 |
| Hall | C17×C53 ⋊ C2×C3 |
| Hall | C3×C53 ⋊ C2×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | D53 |
| commutator, hypocenter | C53 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C53 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C3×C17 | |
16 conjugacy classes of subgroups.
1428 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C17×#6157, C3×#16813360, C3×D17×D53, … |
| maximal normal subgroup of | C3×C17×#6157, C3×#16813360, C3×D17×D53, … |
| maximal quotient of | C3×C17×Dic53, C2×C3×C17×D53, C9×C17×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5406, 2);