Finite Group DatabasebetaFinite Group Databasebeta| order | 15042 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D23×C109⋊C3 |
| unambiguous semidirect product | C23⋊(C2×C109⋊C3) |
| unambiguous semidirect product | (D23×C109)⋊C3 |
| Fitting, socle, derived, Hall | C23×C109 ⋊ C2×C3 |
| Hall | C23×C109⋊C3 ⋊ C2 |
| Hall | D23×C109 ⋊ C3 |
| Sylow | C109 ⋊ C3×D23 |
| Sylow | C23 ⋊ C2×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C109 | C2×C3 |
| LCS | G ▷ C23×C109 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2507 |
507 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D109⋊C3, C2×D23×C109⋊C3 |
| maximal normal subgroup of | D23×D109⋊C3, C2×D23×C109⋊C3 |
| maximal quotient of | Dic23×C109⋊C3, C2×D23×C109⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15042, 11);