Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| automorphism | Aut(G) order 8830080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5110 |
| direct product | C2×D2555 |
| unambiguous semidirect product | (C2×C5)⋊D511 |
| unambiguous semidirect product | (C2×C7)⋊D365 |
| unambiguous semidirect product | (C2×C73)⋊D35 |
| Fitting, socle | C2×C5×C7×C73 ⋊ C2 |
| derived, Hall | C5×C7×C73 ⋊ C22 |
| Hall | C7×C73 ⋊ C2×D5 |
| Hall | C5×C73 ⋊ C2×D7 |
| Sylow | C73 ⋊ C2×D35 |
| Hall | C5×C7 ⋊ C2×D73 |
| Sylow | C7 ⋊ C2×D365 |
| Sylow | C5 ⋊ C2×D511 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2555 |
| commutator, cosocle, hypocenter | C5×C7×C73 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C7×C73 | C2 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
2558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 29);