Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| isoclinism | isoclinic class of D73 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×Dic73 |
| derived, Sylow | C73 ⋊ C4×C5×C7 |
| Hall | C5×C7×C73 ⋊ C4 |
| Hall | C7×C73 ⋊ C4×C5 |
| Hall | C5×C73 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C7 | D73 |
| commutator, hypocenter | C73 | C4×C5×C7 |
| Frattini | C2 | C5×C7×D73 |
| Fitting, socle, prime radical | C2×C5×C7×C73 | C2 |
| cosocle | C2×C73 | C2×C5×C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C5×C7 | |
24 conjugacy classes of subgroups.
2660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C7×Dic73, C5×C7×Dic219, C5×C7×Dic73⋊C3, … |
| maximal normal subgroup of | C3×C5×C7×Dic73, C5×C7×Dic73⋊C3, C5×ΓL(1,𝔽8)×Dic73, … |
| maximal quotient of | C3×C5×C7×Dic73, C5×C7×Dic219 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 2);