Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ((C31⋊C3)⋊C5)⋊D19 |
| unambiguous semidirect product | ((C31⋊C3)⋊D19)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C31 | C2×C3×C5 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 589 |
Polycyclic presentation:
2,3,5,19,31|d^a=d^18,e^a=e^30,e^b=e^25,e^c=e^16184 conjugacy classes — view the full character table.
| maximal subgroup of | D19×AGL(1,𝔽31), C2×((C31⋊C3)⋊C5)⋊D19 |
| maximal normal subgroup of | D19×AGL(1,𝔽31), C2×((C31⋊C3)⋊C5)⋊D19 |
| maximal quotient of | ((C31⋊C3)⋊C5)⋊Dic19, C2×((C31⋊C3)⋊C5)⋊D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 69);