Finite Group DatabasebetaFinite Group Databasebeta| order | 11820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16841102 |
| Fitting, socle, derived, Hall | C3×C5×C197 ⋊ C4 |
| Hall | C5×C197 ⋊ Dic3 |
| Hall | C3×C197 ⋊ Dic5 |
| Sylow | C197 ⋊ Dic15 |
| Hall | C3×C5 ⋊ #11716161 |
| Sylow | C5 ⋊ C3⋊#11716161 |
| Sylow | C3 ⋊ #16841102 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C197 | C4 |
| prime radical, cosocle | C3×C5×D197 | C2 |
| LCS | G ▷ C3×C5×C197 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,197|a^2=b,c^a=c^2,d^a=d^4,e^a=e^183,e^b=e^196753 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16841102, C3×C3⋊#16841102, C3⋊(C3⋊#16841102) |
| maximal normal subgroup of | C3×C3⋊#16841102 |
| maximal quotient of | C9⋊#16841102, C3×C3⋊#16841102, C3⋊(C3⋊#16841102) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11820, 23);