Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D77⋊D33 |
| Fitting, socle, derived, Hall | C3×C7×C112 ⋊ C22 |
| Hall | C7×C112 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D7 |
| Sylow | C112 ⋊ D3×D7 |
| Hall | C3×C7 ⋊ D112 |
| Sylow | C7 ⋊ D11×D33 |
| Sylow | C3 ⋊ D77⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C112 | C22 |
| LCS | G ▷ C3×C7×C112 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,7,11^2|d^a=d^6,e^a=e^10,c^b=c^2,e^b=e^10,f^b=f^10675 conjugacy classes — view the full character table.
| maximal subgroup of | D77⋊D99, (C11⋊AGL(1,𝔽7))⋊D33, #44479133, … |
| maximal normal subgroup of | (C11⋊AGL(1,𝔽7))⋊D33, C3×D77⋊D33 |
| maximal quotient of | D77⋊D99, C3×D77⋊D33, #44479219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 121);