Finite Group DatabasebetaFinite Group Databasebeta| order | 18486 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C13⋊C9)⋊D79 |
| derived, Hall | C13×C79 ⋊ C2×C9 |
| Hall | C79×C13⋊C9 ⋊ C2 |
| Hall | D1027 ⋊ C9 |
| Hall | C13⋊C9 ⋊ D79 |
| Sylow | C79 ⋊ D13⋊C9 |
| Sylow | C13 ⋊ C9×D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C13⋊C3)⋊D79 |
| commutator, hypocenter | C13×C79 | C2×C9 |
| Fitting, socle, cosocle | C3×C13×C79 | C2×C3 |
| prime radical | C3×D1027 | C3 |
| LCS | G ▷ C13×C79 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9243 |
Polycyclic presentation:
2,3,13,79,3|b^3=e,c^a=c^12,d^a=d^78,c^b=c^3843 conjugacy classes — view the full character table.
| maximal subgroup of | D79×D13⋊C9, C2×(C13⋊C9)⋊D79 |
| maximal normal subgroup of | D79×D13⋊C9, C2×(C13⋊C9)⋊D79 |
| maximal quotient of | #49149379, C2×(C13⋊C9)⋊D79 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18486, 27);