Finite Group DatabasebetaFinite Group Databasebeta| order | 17205 |
| isoclinism | isoclinic class of (C31⋊C3)⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×(C31⋊C3)⋊C5 |
| unambiguous semidirect product | (C31⋊C3)⋊(C5×C37) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C3×C37) |
| unambiguous semidirect product | (C37×C31⋊C3)⋊C5 |
| Fitting, socle, Hall | C31×C37 ⋊ C3×C5 |
| derived, Sylow | C31 ⋊ C3×C5×C37 |
| Hall | C37×ΓL(1,𝔽32) ⋊ C3 |
| Hall | C37×C31⋊C3 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C3×C37 |
| Hall | C31⋊C3 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | (C31⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C31 | C3×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C31×C37 | C3×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1147 |
629 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×(C31⋊C3)⋊C5, D37×(C31⋊C3)⋊C5, C37×AGL(1,𝔽31), … |
| maximal normal subgroup of | C2×C37×(C31⋊C3)⋊C5, D37×(C31⋊C3)⋊C5, C37×AGL(1,𝔽31), … |
| maximal quotient of | C2×C37×(C31⋊C3)⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17205, 8);