Finite Group DatabasebetaFinite Group Databasebeta| order | 12070 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D355 |
| unambiguous semidirect product | C5⋊(C17×D71) |
| unambiguous semidirect product | C71⋊(D5×C17) |
| Fitting, socle, Hall | C5×C17×C71 ⋊ C2 |
| derived, Hall | C5×C71 ⋊ C2×C17 |
| Hall | C17×C71 ⋊ D5 |
| Hall | C5×C17 ⋊ D71 |
| Sylow | C71 ⋊ D5×C17 |
| Sylow | C5 ⋊ C17×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D355 |
| commutator, cosocle, hypocenter | C5×C71 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C71 | C2 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
3043 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D5×C17×D71, D17×D355, D85⋊D71, … |
| maximal normal subgroup of | D5×C17×D71, D17×D355, D85⋊D71, … |
| maximal quotient of | C17×Dic355, C2×C17×D355, C3×C17×D355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12070, 7);