Finite Group DatabasebetaFinite Group Databasebeta| order | 4340 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D5×D31 |
| unambiguous semidirect product | (D5×C31)⋊(C2×C7) |
| unambiguous semidirect product | (C5×D31)⋊(C2×C7) |
| unambiguous semidirect product | D155⋊(C2×C7) |
| Fitting, socle, Hall | C5×C7×C31 ⋊ C22 |
| derived, Hall | C5×C31 ⋊ C22×C7 |
| Hall | C7×C31 ⋊ C2×D5 |
| Hall | C5×C7 ⋊ C2×D31 |
| Sylow | C31 ⋊ C2×C7×D5 |
| Sylow | C5 ⋊ C2×C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D5×D31 |
| commutator, cosocle, hypocenter | C5×C31 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C31 | C22 |
| LCS | G ▷ C5×C31 | |
| UCS | C1 ◁ C7 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1085 |
476 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D5×D31⋊C3, D5×#13049954, D5×#13049955, … |
| maximal normal subgroup of | C7×D5×D31⋊C3, D5×#13049954, D5×#13049955, … |
| maximal quotient of | C3×C7×D5×D31, C7×D15×D31, C7×D5×D93, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4340, 24);