Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C7⋊#92150) |
| unambiguous semidirect product | C7⋊(C3⋊#92150) |
| Fitting, socle, derived, Hall | C3×C7×C112 ⋊ C4 |
| Hall | C7×C112 ⋊ Dic3 |
| Hall | C3×C112 ⋊ Dic7 |
| Sylow | C112 ⋊ Dic21 |
| Hall | C3×C7 ⋊ #92150 |
| Sylow | C7 ⋊ C3⋊#92150 |
| Sylow | C3 ⋊ C7⋊#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C112 | C4 |
| prime radical, cosocle | C3×C7×C11⋊D11 | C2 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,11^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^8f^7,f^a=e^8f^3,e^b=e^10,f^b=f^10654 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 112);