Finite Group DatabasebetaFinite Group Databasebeta| order | 2070 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×D15 |
| unambiguous semidirect product | C3⋊(C3×D5×C23) |
| unambiguous semidirect product | C5⋊(C3×D3×C23) |
| Fitting, socle, Hall | C32×C5×C23 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C3×C23 |
| Hall | C32×C23 ⋊ D5 |
| Hall | C5×C23 ⋊ C3×D3 |
| Hall | C32×C5 ⋊ C2×C23 |
| Sylow | C32 ⋊ D5×C23 |
| Sylow | C5 ⋊ C3×D3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C23 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C23 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 34 |
| transitive degree | μt(G) = 690 |
621 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D15×D23, C3×D3×D5×C23, C3×D15⋊D23, … |
| maximal normal subgroup of | C3×D15×D23, C3×D3×D5×C23, C3×D15⋊D23, … |
| maximal quotient of | C3×C23×Dic15, C2×C3×C23×D15, C23×C3⋊(C5⋊AGL(1,𝔽7)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2070, 15);