Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C37⋊(D41⋊C5) |
| unambiguous semidirect product | (C41⋊C5)⋊D37 |
| unambiguous semidirect product | D1517⋊C5 |
| Fitting, socle, derived, Hall | C37×C41 ⋊ C2×C5 |
| Hall | C37×C41⋊C5 ⋊ C2 |
| Hall | D1517 ⋊ C5 |
| Hall | C41⋊C5 ⋊ D37 |
| Sylow | C41 ⋊ C5×D37 |
| Sylow | C37 ⋊ D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C41 | C2×C5 |
| LCS | G ▷ C37×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1517 |
Polycyclic presentation:
2,5,37,41|c^a=c^36,d^a=d^40,d^b=d^10248 conjugacy classes — view the full character table.
| maximal subgroup of | #20258634⋊C5, #20258635⋊C5, D37×D41⋊C5, … |
| maximal normal subgroup of | #20258634⋊C5, #20258635⋊C5, D37×D41⋊C5, … |
| maximal quotient of | Dic1517⋊C5, C2×C37⋊(D41⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 12);