Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C7⋊(C11⋊Dic11)) |
| unambiguous semidirect product | C7⋊(C3⋊(C11⋊Dic11)) |
| unambiguous semidirect product | C11⋊Dic231 |
| derived, Hall | C3×C7×C112 ⋊ C4 |
| Hall | C7×C112 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic7 |
| Sylow | C112 ⋊ Dic21 |
| Hall | C3×C7 ⋊ C11⋊Dic11 |
| Sylow | C7 ⋊ C3⋊(C11⋊Dic11) |
| Sylow | C3 ⋊ C7⋊(C11⋊Dic11) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊(C7⋊(C11⋊D11)) |
| commutator, hypocenter | C3×C7×C112 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C7×C112 | C2 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 ◁ C2 | |
168 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11^2,2|a^2=f,b^a=b^2,c^a=c^6,d^a=d^10,e^a=e^102544 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 62);