Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
No aliases for this group.
| derived, Hall | C7×C112 ⋊ C3×C4 |
| Hall | C7⋊(C11⋊Dic11) ⋊ C3 |
| Hall | C7⋊(C112⋊C3) ⋊ C4 |
| Sylow | C112 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ (C11⋊Dic11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #19099620 |
| 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,c^a=c^6,d^a=d^10,e^a=e^10,c^b=c^2,d^b=d^3e^9,e^b=de^7294 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)⋊((C11⋊Dic11)⋊C3), C3×#23778989, C3⋊#23778989 |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊((C11⋊Dic11)⋊C3), C3×#23778989 |
| maximal quotient of | #44478895, C3×#23778989, C3⋊#23778989 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 41);