Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C13 · Schur multiplier (H2) = C1 |
| direct product | C2×C13×C67⋊C9 |
| unambiguous semidirect product | (C2×C67)⋊(C9×C13) |
| derived, Sylow | C67 ⋊ C2×C9×C13 |
| Hall | C2×C13×C67 ⋊ C9 |
| Hall | C13×C67 ⋊ C2×C9 |
| Hall | C2×C67 ⋊ C9×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C13 | C67⋊C3 |
| commutator, hypocenter | C67 | C2×C9×C13 |
| Frattini | C3 | C2×C13×C67⋊C3 |
| Fitting, socle, prime radical | C2×C3×C13×C67 | C3 |
| cosocle | C3×C67 | C2×C3×C13 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C2×C3×C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15678 |
1950 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C13×C67⋊C9, C13×Dic67⋊C9, Dic13×C67⋊C9, … |
| maximal normal subgroup of | C4×C13×C67⋊C9, C13×Dic67⋊C9, Dic13×C67⋊C9, … |
| maximal quotient of | C4×C13×C67⋊C9, C22×C13×C67⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 2);