Finite Group DatabasebetaFinite Group Databasebeta| order | 10140 |
| automorphism | Aut(G) order 6327360 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D5070 |
| direct product | C2×D2535 |
| unambiguous semidirect product | (C2×C3)⋊D845 |
| unambiguous semidirect product | (C2×C5)⋊D507 |
| unambiguous semidirect product | (C2×C169)⋊D15 |
| Fitting | C2×C3×C5×C169 ⋊ C2 |
| derived, Hall | C3×C5×C169 ⋊ C22 |
| Hall | C5×C169 ⋊ C2×D3 |
| Hall | C3×C169 ⋊ C2×D5 |
| Sylow | C169 ⋊ C2×D15 |
| Hall | C3×C5 ⋊ C2×D169 |
| Sylow | C5 ⋊ C2×D507 |
| Sylow | C3 ⋊ C2×D845 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2535 |
| commutator, cosocle, hypocenter | C3×C5×C169 | C22 |
| Frattini | C13 | C2×D195 |
| Fitting | C2×C3×C5×C169 | C2 |
| socle | C2×C3×C5×C13 | D13 |
| LCS | G ▷ C3×C5×C169 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
2538 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D7605, C2×C3⋊(C5⋊(D169⋊C3)), D3×D2535, … |
| maximal normal subgroup of | C2×C3⋊(C5⋊(D169⋊C3)), C2×C3×D2535, D10140 |
| maximal quotient of | C2×D7605, D3×D2535, C2×C3⋊D2535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10140, 52);