Finite Group DatabasebetaFinite Group Databasebeta| order | 940 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C47 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×C47 |
| unambiguous semidirect product | C5⋊(C22×C47) |
| unambiguous semidirect product | (C2×C5)⋊(C2×C47) |
| Fitting, socle | C2×C5×C47 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C47 |
| Hall | C5×C47 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C47 | D5 |
| commutator, cosocle, hypocenter | C5 | C22×C47 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C47 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C2×C47 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 470 |
376 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×Dic47, #14273519, #14273521, … |
| maximal normal subgroup of | D5×Dic47, #14273519, #14273521, … |
| maximal quotient of | Dic10×C47, C4×D5×C47, D20×C47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(940, 9);