Finite Group DatabasebetaFinite Group Databasebeta| order | 18669 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C49 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C127⋊C3)⋊C49 |
| unambiguous semidirect product | (C127⋊C49)⋊C3 |
| derived, Sylow | C127 ⋊ C3×C49 |
| Hall | C127⋊C49 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C49 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C7 | (C127⋊C3)⋊C7 |
| commutator, hypocenter | C127 | C3×C49 |
| Fitting, socle, cosocle | C7×C127 | C3×C7 |
| prime radical | C7×C127⋊C3 | C7 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6223 |
Polycyclic presentation:
3,7,127,7|b^7=d,c^a=c^107,c^b=c^4189 conjugacy classes — view the full character table.
| maximal subgroup of | C2×(C127⋊C3)⋊C49, (D127⋊C3)⋊C49 |
| maximal normal subgroup of | C2×(C127⋊C3)⋊C49, (D127⋊C3)⋊C49 |
| maximal quotient of | C2×(C127⋊C3)⋊C49 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18669, 2);