Finite Group DatabasebetaFinite Group Databasebeta| order | 10860 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16813738 |
| Fitting, socle, derived, Hall | C3×C5×C181 ⋊ C4 |
| Hall | C5×C181 ⋊ Dic3 |
| Hall | C3×C181 ⋊ AGL(1,𝔽5) |
| Sylow | C181 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #10624382 |
| Sylow | C5 ⋊ C3⋊#10624382 |
| Sylow | C3 ⋊ #16813738 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C181 | C4 |
| prime radical, cosocle | C3×D905 | C2 |
| LCS | G ▷ C3×C5×C181 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,181|a^2=b,c^a=c^2,d^a=d^2,e^a=e^19,d^b=d^4,e^b=e^180684 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16813738, C3⋊(#16813738⋊C3), C3×C3⋊#16813738, … |
| maximal normal subgroup of | C3⋊(#16813738⋊C3), C3×C3⋊#16813738 |
| maximal quotient of | C9⋊#16813738, C3×C3⋊#16813738, C3⋊(C3⋊#16813738) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10860, 53);