Finite Group DatabasebetaFinite Group Databasebeta| order | 17205 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×ΓL(1,𝔽32) |
| unambiguous semidirect product | C37⋊(C3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×C37⋊C3)⋊C5 |
| Fitting, socle, derived, Hall | C31×C37 ⋊ C3×C5 |
| Hall | C37×ΓL(1,𝔽32) ⋊ C3 |
| Hall | C31×C37⋊C3 ⋊ C5 |
| Sylow | C37 ⋊ C3×ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C5×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C37 | C3×C5 |
| LCS | G ▷ C31×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1147 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C37⋊C3×ΓL(1,𝔽32), ΓL(1,𝔽32)×D37⋊C3, C37⋊C3×D31⋊C5, … |
| maximal normal subgroup of | C2×C37⋊C3×ΓL(1,𝔽32), ΓL(1,𝔽32)×D37⋊C3, C37⋊C3×D31⋊C5, … |
| maximal quotient of | C2×C37⋊C3×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17205, 7);