Finite Group DatabasebetaFinite Group Databasebeta| order | 15042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D327 |
| unambiguous semidirect product | C3⋊(C23×D109) |
| unambiguous semidirect product | C109⋊(D3×C23) |
| Fitting, socle, Hall | C3×C23×C109 ⋊ C2 |
| derived, Hall | C3×C109 ⋊ C2×C23 |
| Hall | C23×C109 ⋊ D3 |
| Sylow | C109 ⋊ D3×C23 |
| Hall | C3×C23 ⋊ D109 |
| Sylow | C3 ⋊ C23×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D327 |
| commutator, cosocle, hypocenter | C3×C109 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C23×C109 | C2 |
| LCS | G ▷ C3×C109 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7521 |
3795 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C23×D109, D23×D327, D69⋊D109, … |
| maximal normal subgroup of | D3×C23×D109, D23×D327, D69⋊D109, … |
| maximal quotient of | C23×Dic327, C2×C23×D327 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15042, 7);