Finite Group DatabasebetaFinite Group Databasebeta| order | 9434 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D53 |
| unambiguous semidirect product | C53⋊(C2×C89) |
| Fitting, socle, Hall | C53×C89 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D53 |
| commutator, hypocenter | C53 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C53×C89 | C2 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C89 | |
8 conjugacy classes of subgroups.
2492 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C89×#6157, #34038253, D53×D89, … |
| maximal normal subgroup of | C89×#6157, #34038253, D53×D89, … |
| maximal quotient of | C89×Dic53, C2×C89×D53, C3×C89×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9434, 1);