Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C11⋊Dic11)⋊ΓL(1,𝔽8) |
| derived, Hall | C7×C112 ⋊ C3×C4 |
| Hall | C7×C11⋊Dic11 ⋊ C3 |
| Hall | C7⋊(C112⋊C3) ⋊ C4 |
| Hall | C11⋊Dic11 ⋊ ΓL(1,𝔽8) |
| Sylow | C112 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ (C11⋊Dic11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C11⋊D11)⋊ΓL(1,𝔽8) |
| commutator, hypocenter | C7×C112 | C3×C4 |
| Fitting, socle, cosocle | C2×C7×C112 | C2×C3 |
| prime radical | C2×C7⋊(C112⋊C3) | C2 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11^2,2|a^2=f,d^a=d^10,e^a=e^10,c^b=c^2,d^b=d^3e^9,e^b=de^7300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 45);