Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic181⋊C3)⋊C5 |
| unambiguous semidirect product | (Dic181⋊C5)⋊C3 |
| derived, Sylow | C181 ⋊ C3×C4×C5 |
| Hall | Dic181⋊C5 ⋊ C3 |
| Hall | (C181⋊C3)⋊C5 ⋊ C4 |
| Hall | Dic181⋊C3 ⋊ C5 |
| Hall | C181⋊C5 ⋊ C3×C4 |
| Hall | Dic181 ⋊ C3×C5 |
| Hall | C181⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (D181⋊C3)⋊C5 |
| commutator, hypocenter | C181 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C181 | C2×C3×C5 |
| prime radical | C2×(C181⋊C3)⋊C5 | C2 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,181,2|a^2=e,d^a=d^180,d^b=d^48,d^c=d^5972 conjugacy classes — view the full character table.
| maximal subgroup of | #20266783⋊C5, C3×(Dic181⋊C3)⋊C5, C3⋊((Dic181⋊C3)⋊C5) |
| maximal normal subgroup of | #20266783⋊C5, C3×(Dic181⋊C3)⋊C5 |
| maximal quotient of | #20266765⋊C5, C3×(Dic181⋊C3)⋊C5, C3⋊((Dic181⋊C3)⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 18);