Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C7⋊#64408 |
| unambiguous semidirect product | C7⋊(C5×#64408) |
| Fitting, socle, Hall | C5×C7×C73 ⋊ C4 |
| derived, Hall | C7×C73 ⋊ C4×C5 |
| Hall | C5×C73 ⋊ Dic7 |
| Sylow | C73 ⋊ C5×Dic7 |
| Hall | C5×C7 ⋊ #64408 |
| Sylow | C7 ⋊ C5×#64408 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊#64408 |
| commutator, hypocenter | C7×C73 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C73 | C4 |
| prime radical | C5×C7×D73 | C2 |
| cosocle | C7×D73 | C2×C5 |
| LCS | G ▷ C7×C73 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
680 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#20259496, C5×#20259497, C5×ΓL(1,𝔽8)⋊#64408, … |
| maximal normal subgroup of | C5×#20259496, C5×#20259497, C5×ΓL(1,𝔽8)⋊#64408, … |
| maximal quotient of | C3×C5×C7⋊#64408, C5×C3⋊(C7⋊#64408) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 11);