Finite Group DatabasebetaFinite Group Databasebeta| order | 18190 |
| isoclinism | isoclinic class of D85 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×D85 |
| unambiguous semidirect product | C5⋊(D17×C107) |
| unambiguous semidirect product | C17⋊(D5×C107) |
| Fitting, socle, Hall | C5×C17×C107 ⋊ C2 |
| derived, Hall | C5×C17 ⋊ C2×C107 |
| Hall | C17×C107 ⋊ D5 |
| Hall | C5×C107 ⋊ D17 |
| Sylow | C17 ⋊ D5×C107 |
| Sylow | C5 ⋊ D17×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D85 |
| commutator, cosocle, hypocenter | C5×C17 | C2×C107 |
| Frattini | C1 | G |
| Fitting, socle | C5×C17×C107 | C2 |
| LCS | G ▷ C5×C17 | |
| UCS | C1 ◁ C107 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9095 |
4708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C107×#66775, C107⋊#66775, C107×#66776, … |
| maximal normal subgroup of | C107×#66775, C107⋊#66775, C107×#66776, … |
| maximal quotient of | C107×Dic85, C2×C107×D85 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18190, 7);