Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C11⋊AGL(1,𝔽7))⋊D11 |
| unambiguous semidirect product | (D77⋊D11)⋊C3 |
| Fitting, socle, derived, Hall | C7×C112 ⋊ C22×C3 |
| Hall | D77⋊D11 ⋊ C3 |
| Hall | C112×ΓL(1,𝔽8) ⋊ C22 |
| Sylow | C112 ⋊ C2×AGL(1,𝔽7) |
| Hall | ΓL(1,𝔽8) ⋊ D112 |
| Sylow | C7 ⋊ C3×D112 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C112 | C22×C3 |
| LCS | G ▷ 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,e^b=e^10,f^b=f^10,d^c=d^2209 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 70);