Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C2×C3×C13×C67⋊C3 |
| unambiguous semidirect product | (C2×C67)⋊(C32×C13) |
| unambiguous semidirect product | (C2×C3×C67)⋊(C3×C13) |
| Fitting, socle | C2×C3×C13×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C2×C32×C13 |
| Hall | C2×C13×C67 ⋊ C32 |
| Hall | C13×C67 ⋊ C2×C32 |
| Hall | C2×C67 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C13×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C3×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5226 |
1950 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 61);