Finite Group DatabasebetaFinite Group Databasebeta| order | 11470 |
| isoclinism | isoclinic class of D31⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D31⋊C5 |
| unambiguous semidirect product | D31⋊(C5×C37) |
| unambiguous semidirect product | ΓL(1,𝔽32)⋊(C2×C37) |
| unambiguous semidirect product | (C37×D31)⋊C5 |
| Fitting, socle, Hall | C31×C37 ⋊ C2×C5 |
| derived, Sylow | C31 ⋊ C2×C5×C37 |
| Hall | C37×ΓL(1,𝔽32) ⋊ C2 |
| Hall | C37×D31 ⋊ C5 |
| Hall | ΓL(1,𝔽32) ⋊ C2×C37 |
| Hall | D31 ⋊ C5×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D31⋊C5 |
| commutator, cosocle, hypocenter | C31 | C2×C5×C37 |
| Frattini | C1 | G |
| Fitting, socle | C31×C37 | C2×C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
481 conjugacy classes — view the full character table.
| maximal subgroup of | D37×D31⋊C5, C2×C37×D31⋊C5, C3×C37×D31⋊C5, … |
| maximal normal subgroup of | D37×D31⋊C5, C2×C37×D31⋊C5, C3×C37×D31⋊C5, … |
| maximal quotient of | C37×Dic31⋊C5, C2×C37×D31⋊C5, C3×C37×D31⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11470, 11);