Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C5×C169 ⋊ C22×C3 |
| Hall | D5×D169 ⋊ C3 |
| Hall | C5×C169⋊C3 ⋊ C22 |
| Hall | C169⋊C3 ⋊ C2×D5 |
| Sylow | C169 ⋊ C2×C3×D5 |
| Sylow | C5 ⋊ C2×D169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C169 | C22×C3 |
| Frattini | C13 | D5×D13⋊C3 |
| socle | C5×C13 | C2×D13⋊C3 |
| LCS | G ▷ C5×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
136 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×D169⋊C3, D15×D169⋊C3, D5×C3⋊(D169⋊C3), … |
| maximal normal subgroup of | C3×D5×D169⋊C3 |
| maximal quotient of | D5×D169⋊C9, C3×D5×D169⋊C3, D15×D169⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 20);