Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| isoclinism | isoclinic class of D185 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D185 |
| unambiguous semidirect product | C5⋊(C41×D37) |
| unambiguous semidirect product | C37⋊(D5×C41) |
| Fitting, socle, Hall | C5×C37×C41 ⋊ C2 |
| derived, Hall | C5×C37 ⋊ C2×C41 |
| Hall | C37×C41 ⋊ D5 |
| Hall | C5×C41 ⋊ D37 |
| Sylow | C37 ⋊ D5×C41 |
| Sylow | C5 ⋊ C41×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D185 |
| commutator, cosocle, hypocenter | C5×C37 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C41 | C2 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7585 |
3854 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C41×#10625191, #44476847, C41×#10625192, … |
| maximal normal subgroup of | C41×#10625191, #44476847, C41×#10625192, … |
| maximal quotient of | C41×Dic185, C2×C41×D185 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 8);