Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D313⋊C9 |
| unambiguous semidirect product | (C313⋊C9)⋊C2 |
| derived, Sylow | C313 ⋊ C2×C9 |
| Hall | C313⋊C9 ⋊ C2 |
| Hall | D313 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D313⋊C3 |
| commutator, hypocenter | C313 | C2×C9 |
| Fitting, socle | C3×C313 | C2×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,313,3|b^3=d,c^a=c^312,c^b=c^214174 conjugacy classes — view the full character table.
| maximal subgroup of | #11929411⋊C9, C2×D313⋊C9, C5×D313⋊C9, … |
| maximal normal subgroup of | #11929411⋊C9, C2×D313⋊C9, C5×D313⋊C9 |
| maximal quotient of | Dic313⋊C9, C2×D313⋊C9, C5×D313⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 2);