Finite Group DatabasebetaFinite Group Databasebeta| order | 18369 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C157⋊C9)⋊C13 |
| unambiguous semidirect product | (C157⋊C13)⋊C9 |
| derived, Sylow | C157 ⋊ C9×C13 |
| Hall | C157⋊C13 ⋊ C9 |
| Hall | C157⋊C9 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C157⋊C3)⋊C13 |
| commutator, hypocenter | C157 | C9×C13 |
| Fitting, socle, cosocle | C3×C157 | C3×C13 |
| prime radical | C3×C157⋊C13 | C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1413 |
Polycyclic presentation:
3,13,157,3|a^3=d,c^a=c^12,c^b=c^130129 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C157⋊C9)⋊C13, (D157⋊C9)⋊C13 |
| maximal normal subgroup of | C2×(C157⋊C9)⋊C13, (D157⋊C9)⋊C13 |
| maximal quotient of | C2×(C157⋊C9)⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18369, 2);