Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of D105 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic105 |
| unambiguous semidirect product | C3⋊(C3×Dic35) |
| derived | C3×C5×C7 ⋊ C3×C4 |
| Hall | C32×C5×C7 ⋊ C4 |
| Hall | C32×C7 ⋊ Dic5 |
| Hall | C32×C5 ⋊ Dic7 |
| Hall | C5×C7 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic35 |
| Sylow | C7 ⋊ C3×Dic15 |
| Sylow | C5 ⋊ C3×Dic21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D105 |
| commutator, hypocenter | C3×C5×C7 | C3×C4 |
| Frattini | C2 | C3×D105 |
| Fitting, socle, prime radical | C2×C32×C5×C7 | C2 |
| cosocle | C2×C3×C5×C7 | C2×C3 |
| LCS | G ▷ C3×C5×C7 | |
| UCS | C1 ◁ C2×C3 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 420 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×Dic105, C3×Dic1155, C3⋊#19129703, … |
| maximal normal subgroup of | C3×C11×Dic105, C3×C13×Dic105, C3×C17×Dic105, … |
| maximal quotient of | C3×C11×Dic105, C3×Dic1155, C3⋊#19129703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 55);