Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13091732 |
| Fitting, socle, Hall | C5×C7×C73 ⋊ C4 |
| derived, Hall | C5×C73 ⋊ C4×C7 |
| Hall | C7×C73 ⋊ AGL(1,𝔽5) |
| Sylow | C73 ⋊ C7×AGL(1,𝔽5) |
| Hall | C5×C7 ⋊ #64408 |
| Sylow | C5 ⋊ C7×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13091732 |
| commutator, hypocenter | C5×C73 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C73 | C4 |
| prime radical | C7×D365 | C2 |
| cosocle | D365 | C2×C7 |
| LCS | G ▷ C5×C73 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
665 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#13091732⋊C3, #44501316, #44501318, … |
| maximal normal subgroup of | C7×#13091732⋊C3, #44501316, #44501318, … |
| maximal quotient of | C3×C7×#13091732, C7×C3⋊#13091732 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 14);