Finite Group DatabasebetaFinite Group Databasebeta| order | 1260 |
| isoclinism | isoclinic class of C3⋊D105 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D105 |
| unambiguous semidirect product | (C2×C3)⋊D105 |
| unambiguous semidirect product | (C2×C5)⋊(C3⋊D21) |
| unambiguous semidirect product | (C2×C7)⋊(C3⋊D15) |
| Fitting, socle | C2×C32×C5×C7 ⋊ C2 |
| derived, Hall | C32×C5×C7 ⋊ C22 |
| Hall | C32×C7 ⋊ C2×D5 |
| Hall | C32×C5 ⋊ C2×D7 |
| Hall | C5×C7 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ C2×D35 |
| Sylow | C7 ⋊ C2×C3⋊D15 |
| Sylow | C5 ⋊ C2×C3⋊D21 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D105 |
| commutator, cosocle, hypocenter | C32×C5×C7 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C5×C7 | C2 |
| LCS | G ▷ C32×C5×C7 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 630 |
318 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×C3⋊D105, C2×C3⋊D1155, C2×C11×C3⋊D105, … |
| maximal normal subgroup of | C2×C11×C3⋊D105, C2×C13×C3⋊D105, C2×C17×C3⋊D105, … |
| maximal quotient of | D11×C3⋊D105, C2×C3⋊D1155, C2×C11×C3⋊D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1260, 130);