Finite Group DatabasebetaFinite Group Databasebeta| order | 15170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D37×C41⋊C5 |
| unambiguous semidirect product | C37⋊(C2×C41⋊C5) |
| unambiguous semidirect product | (C41×D37)⋊C5 |
| Fitting, socle, derived, Hall | C37×C41 ⋊ C2×C5 |
| Hall | C37×C41⋊C5 ⋊ C2 |
| Hall | C41×D37 ⋊ C5 |
| Sylow | C41 ⋊ C5×D37 |
| Sylow | C37 ⋊ C2×C41⋊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 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #20258636⋊C5, #3866×C41⋊C5, D37×D41⋊C5, … |
| maximal normal subgroup of | #20258636⋊C5, #3866×C41⋊C5, D37×D41⋊C5, … |
| maximal quotient of | Dic37×C41⋊C5, C2×D37×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15170, 11);