Finite Group DatabasebetaFinite Group Databasebeta| order | 5394 |
| automorphism | Aut(G) order 4530960 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D2697 |
| unambiguous semidirect product | C3⋊D899 |
| unambiguous semidirect product | C29⋊D93 |
| unambiguous semidirect product | C31⋊D87 |
| Fitting, socle, derived, Hall | C3×C29×C31 ⋊ C2 |
| Hall | C29×C31 ⋊ D3 |
| Hall | C3×C31 ⋊ D29 |
| Hall | C3×C29 ⋊ D31 |
| Sylow | C31 ⋊ D87 |
| Sylow | C29 ⋊ D93 |
| Sylow | C3 ⋊ D899 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C29×C31 | C2 |
| LCS | G ▷ C3×C29×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,31|b^a=b^2,c^a=c^28,d^a=d^301350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8091, C3⋊(C29⋊(D31⋊C3)), C3⋊D2697, … |
| maximal normal subgroup of | C3⋊(C29⋊(D31⋊C3)), C3×D2697, C5×D2697, … |
| maximal quotient of | D8091, C3⋊D2697, C3×D2697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5394, 9);