Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×#64408 |
| Fitting, socle, Hall | C5×C7×C73 ⋊ C4 |
| derived, Sylow | C73 ⋊ C4×C5×C7 |
| Hall | C7×C73 ⋊ C4×C5 |
| Hall | C5×C73 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | #64408 |
| commutator, hypocenter | C73 | C4×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C73 | C4 |
| prime radical | C5×C7×D73 | C2 |
| cosocle | D73 | C2×C5×C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C5×C7 | |
24 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×#64408⋊C3, C5×#20259502, C5×#20259503, … |
| maximal normal subgroup of | C5×C7×#64408⋊C3, C5×#20259502, C5×#20259503, … |
| maximal quotient of | C3×C5×C7×#64408, C5×C7×C3⋊#64408 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 10);