Finite Group DatabasebetaFinite Group Databasebeta| order | 10220 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D365 |
| unambiguous semidirect product | (C5×D7)⋊D73 |
| unambiguous semidirect product | (D7×C73)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C73 ⋊ C22 |
| Hall | C7×C73 ⋊ C2×D5 |
| Hall | C5×C73 ⋊ C2×D7 |
| Sylow | C73 ⋊ D5×D7 |
| Hall | C5×C7 ⋊ C2×D73 |
| Sylow | C7 ⋊ C2×D365 |
| Sylow | C5 ⋊ D7×D73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C73 | C22 |
| LCS | G ▷ C5×C7×C73 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
920 conjugacy classes — view the full character table.
| maximal subgroup of | #15690445⋊D5, #15690446⋊D5, AGL(1,𝔽7)×D365, … |
| maximal normal subgroup of | #15690445⋊D5, #15690446⋊D5, AGL(1,𝔽7)×D365, … |
| maximal quotient of | C3×D7×D365, D7×D1095, D21×D365, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10220, 26);