Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | D19⋊C3×ΓL(1,𝔽32) |
| unambiguous semidirect product | D19⋊(C3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D19⋊C3)⋊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 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D31⋊C5, C2×D19⋊C3×ΓL(1,𝔽32) |
| maximal normal subgroup of | D19⋊C3×D31⋊C5, C2×D19⋊C3×ΓL(1,𝔽32) |
| maximal quotient of | ΓL(1,𝔽32)×(C19⋊C3)⋊C4, C2×D19⋊C3×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 66);