Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C41 · Schur multiplier (H2) = C1 |
| direct product | C5×C41×D37 |
| unambiguous semidirect product | C37⋊(C2×C5×C41) |
| Fitting, socle, Hall | C5×C37×C41 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C5×C41 |
| Hall | C37×C41 ⋊ C2×C5 |
| Hall | C5×C37 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C41 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C5×C41 |
| Frattini | C1 | G |
| Fitting, socle | C5×C37×C41 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C5×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7585 |
4100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C41×#3866, C5×#20258636, C5×D37×D41, … |
| maximal normal subgroup of | C5×C41×#3866, C5×#20258636, C5×D37×D41, … |
| maximal quotient of | C5×C41×Dic37, C2×C5×C41×D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 4);