Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| isoclinism | isoclinic class of D61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D61⋊C3 |
| unambiguous semidirect product | D61⋊(C3×C43) |
| unambiguous semidirect product | (C61⋊C3)⋊(C2×C43) |
| Fitting, socle, Hall | C43×C61 ⋊ C2×C3 |
| derived, Sylow | C61 ⋊ C2×C3×C43 |
| Hall | C43×C61⋊C3 ⋊ C2 |
| Hall | C43×D61 ⋊ C3 |
| Hall | C61⋊C3 ⋊ C2×C43 |
| Hall | D61 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D61⋊C3 |
| commutator, cosocle, hypocenter | C61 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C61 | C2×C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43×#6923⋊C3, #44538360, D43×D61⋊C3, … |
| maximal normal subgroup of | C43×#6923⋊C3, #44538360, D43×D61⋊C3, … |
| maximal quotient of | C43×Dic61⋊C3, C2×C43×D61⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 13);