Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1517 |
| unambiguous semidirect product | C37⋊(C5×D41) |
| Fitting, socle, Hall | C5×C37×C41 ⋊ C2 |
| derived, Hall | C37×C41 ⋊ C2×C5 |
| Hall | C5×C41 ⋊ D37 |
| Hall | C5×C37 ⋊ D41 |
| Sylow | C41 ⋊ C5×D37 |
| Sylow | C37 ⋊ C5×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1517 |
| commutator, cosocle, hypocenter | C37×C41 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C41 | C2 |
| LCS | G ▷ C37×C41 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7585 |
3800 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20258634, C5×#20258635, C5×D37×D41, … |
| maximal normal subgroup of | C5×#20258634, C5×#20258635, C5×D37×D41, … |
| maximal quotient of | C5×Dic1517, C2×C5×D1517 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 5);