Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D35⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D35⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C5×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×D5 |
| Hall | C32×C5 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ D5×D7 |
| Sylow | C7 ⋊ D5×C3⋊D3 |
| Sylow | C5 ⋊ D7×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C7 | C22 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 315 |
Polycyclic presentation:
2^2,3^2,5,7|e^a=e^4,f^a=f^6,c^b=c^2,d^b=d^2,e^b=e^496 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 106);