Finite Group DatabasebetaFinite Group Databasebeta| order | 10164 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C11 |
| direct product | C7×#13089721 |
| Fitting, socle, Hall | C7×C112 ⋊ Dic3 |
| derived, Hall | C112⋊C3 ⋊ C4×C7 |
| Hall | C7×C112⋊C3 ⋊ C4 |
| Sylow | C112 ⋊ C7×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13089721 |
| commutator, hypocenter | C112⋊C3 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C112 | Dic3 |
| prime radical | C7×(C11⋊D11)⋊C3 | C2 |
| cosocle | (C11⋊D11)⋊C3 | C2×C7 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C7 | |
32 conjugacy classes of subgroups.
112 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#13089721, C3×C7×#13089721, C7×C3⋊#13089721 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#13089721, C3×C7×#13089721 |
| maximal quotient of | C7×#17983714, C3×C7×#13089721, C7×C3⋊#13089721 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10164, 65);