Finite Group DatabasebetaFinite Group Databasebeta| order | 17670 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D57×ΓL(1,𝔽32) |
| unambiguous semidirect product | C3⋊(D19×ΓL(1,𝔽32)) |
| unambiguous semidirect product | C19⋊(D3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D57)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C31 | C2×C5 |
| LCS | G ▷ C3×C19×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1767 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D57×D31⋊C5, D57⋊(D31⋊C5), D3×D19×ΓL(1,𝔽32), … |
| maximal normal subgroup of | D57×D31⋊C5, D57⋊(D31⋊C5), D3×D19×ΓL(1,𝔽32), … |
| maximal quotient of | ΓL(1,𝔽32)×Dic57, C2×D57×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17670, 31);