Finite Group DatabasebetaFinite Group Databasebeta| order | 11970 |
| isoclinism | isoclinic class of C3⋊D57 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C3 |
| direct product | C5×C7×C3⋊D57 |
| unambiguous semidirect product | C3⋊(C5×C7×D57) |
| unambiguous semidirect product | C19⋊(C5×C7×C3⋊D3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | C3⋊D57 |
| commutator, cosocle, hypocenter | C32×C19 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C19 | C2 |
| LCS | G ▷ C32×C19 | |
| UCS | C1 ◁ C5×C7 | |
96 conjugacy classes of subgroups.
3045 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×C7×D57, C5×D21⋊D57, C7×D15⋊D57, … |
| maximal normal subgroup of | C5×D3×C7×D57, C5×D21⋊D57, C7×D15⋊D57, … |
| maximal quotient of | C5×C7×C3⋊Dic57, C2×C5×C7×C3⋊D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11970, 152);