Finite Group DatabasebetaFinite Group Databasebeta| order | 15678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D13×C67⋊C9 |
| derived, Hall | C13×C67 ⋊ C2×C9 |
| Hall | C13×C67⋊C9 ⋊ C2 |
| Hall | D13×C67 ⋊ C9 |
| Sylow | C67 ⋊ C9×D13 |
| Sylow | C13 ⋊ C2×C67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D13×C67⋊C3 |
| commutator, hypocenter | C13×C67 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C67 | C2×C3 |
| prime radical | C3×D13×C67 | C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C67⋊C9)⋊#261, #261×C67⋊C9, D13×D67⋊C9, … |
| maximal normal subgroup of | (C67⋊C9)⋊#261, #261×C67⋊C9, D13×D67⋊C9, … |
| maximal quotient of | Dic13×C67⋊C9, C2×D13×C67⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15678, 17);