Finite Group DatabasebetaFinite Group Databasebeta| order | 954 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D53 |
| unambiguous semidirect product | C53⋊(C2×C9) |
| Fitting, Hall | C9×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D53 |
| commutator, hypocenter | C53 | C2×C9 |
| Frattini | C3 | C3×D53 |
| Fitting | C9×C53 | C2 |
| socle, cosocle | C3×C53 | C2×C3 |
| prime radical | C3×D53 | C3 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 477 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#6157, C9⋊#6157, D9×D53, … |
| maximal normal subgroup of | C9×#6157, C9⋊#6157, D9×D53, … |
| maximal quotient of | C9×Dic53, C2×C9×D53, C5×C9×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(954, 2);