Finite Group DatabasebetaFinite Group Databasebeta| order | 5634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D313 |
| Fitting, Hall | C9×C313 ⋊ C2 |
| derived, Sylow | C313 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D313 |
| commutator, hypocenter | C313 | C2×C9 |
| Frattini | C3 | C3×D313 |
| Fitting | C9×C313 | C2 |
| socle | C3×C313 | C2×C3 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
1422 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#11929411, C9⋊#11929411, D9×D313, … |
| maximal normal subgroup of | C9×#11929411, C9⋊#11929411, D9×D313, … |
| maximal quotient of | C9×Dic313, C2×C9×D313, C5×C9×D313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5634, 5);