Finite Group DatabasebetaFinite Group Databasebeta| order | 1170 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D39 |
| unambiguous semidirect product | C3⋊(C3×C5×D13) |
| Fitting, socle, Hall | C32×C5×C13 ⋊ C2 |
| derived | C3×C13 ⋊ C2×C3×C5 |
| Hall | C32×C13 ⋊ C2×C5 |
| Hall | C5×C13 ⋊ C3×D3 |
| Hall | C32×C5 ⋊ D13 |
| Sylow | C13 ⋊ C3×C5×D3 |
| Sylow | C32 ⋊ C5×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D39 |
| commutator, cosocle, hypocenter | C3×C13 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C13 | C2 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C3×C5 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 390 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D3×D13, C3×D5×D39, C3×D15⋊D13, … |
| maximal normal subgroup of | C3×C5×D3×D13, C3×D5×D39, C3×D15⋊D13, … |
| maximal quotient of | C3×C5×Dic39, C2×C3×C5×D39, C3×C3⋊(C13⋊AGL(1,𝔽11)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1170, 25);