Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D61×C43⋊C3 |
| Fitting, socle, derived, Hall | C43×C61 ⋊ C2×C3 |
| Hall | C61×C43⋊C3 ⋊ C2 |
| Hall | C43×D61 ⋊ C3 |
| Sylow | C61 ⋊ C2×C43⋊C3 |
| Sylow | C43 ⋊ C3×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C61 | C2×C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
544 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C43⋊C3)⋊#6923, D61×D43⋊C3, C43⋊C3×#6923, … |
| maximal normal subgroup of | (C43⋊C3)⋊#6923, D61×D43⋊C3, C43⋊C3×#6923, … |
| maximal quotient of | C43⋊C3×Dic61, C2×D61×C43⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 14);