Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D39⋊D65 |
| Fitting, socle, derived, Hall | C3×C5×C132 ⋊ C22 |
| Hall | C5×C132 ⋊ C2×D3 |
| Hall | C3×C132 ⋊ C2×D5 |
| Sylow | C132 ⋊ D3×D5 |
| Hall | C3×C5 ⋊ D132 |
| Sylow | C5 ⋊ D39⋊D13 |
| Sylow | C3 ⋊ D13×D65 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C132 | C22 |
| LCS | G ▷ C3×C5×C132 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,13^2|d^a=d^4,e^a=e^12,f^a=f^12,c^b=c^2,f^b=f^12696 conjugacy classes — view the full character table.
| maximal subgroup of | #15690146⋊D5, D117⋊D65, #44478101, … |
| maximal normal subgroup of | (C3⋊(D13⋊C3))⋊D65, #44478113, #44478128, … |
| maximal quotient of | D117⋊D65, C3×D39⋊D65, D39⋊D195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 254);