Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊((C181⋊C3)⋊C5) |
| unambiguous semidirect product | (C181⋊C5)⋊A4 |
| unambiguous semidirect product | (C22⋊(C181⋊C3))⋊C5 |
| Fitting, socle, derived, Hall | C22×C181 ⋊ C3×C5 |
| Hall | C22×C181⋊C5 ⋊ C3 |
| Hall | C22⋊(C181⋊C3) ⋊ C5 |
| Hall | C181⋊C5 ⋊ A4 |
| Sylow | C181 ⋊ C5×A4 |
| Sylow | C22 ⋊ (C181⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C181 | C3×C5 |
| LCS | G ▷ C22×C181 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
3,5,2^2,181|c^a=d,d^a=cd,e^a=e^132,e^b=e^5968 conjugacy classes — view the full character table.
| maximal subgroup of | A4×(C181⋊C3)⋊C5, C3×C22⋊((C181⋊C3)⋊C5) |
| maximal normal subgroup of | A4×(C181⋊C3)⋊C5, C3×C22⋊((C181⋊C3)⋊C5) |
| maximal quotient of | C22⋊(#13108656⋊C5), C3×C22⋊((C181⋊C3)⋊C5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 26);