Finite Group DatabasebetaFinite Group Databasebeta| order | 4564 |
| isoclinism | isoclinic class of D163 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D163 |
| unambiguous semidirect product | C163⋊(C22×C7) |
| unambiguous semidirect product | (C2×C163)⋊(C2×C7) |
| Fitting, socle | C2×C7×C163 ⋊ C2 |
| derived, Sylow | C163 ⋊ C22×C7 |
| Hall | C7×C163 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D163 |
| commutator, cosocle, hypocenter | C163 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C163 | C2 |
| LCS | G ▷ C163 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2282 |
1162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×D163⋊C3, C2×#20292068, C2×#20292069, … |
| maximal normal subgroup of | C2×C7×D163⋊C3, C2×#20292068, C2×#20292069, … |
| maximal quotient of | D3×C7×D163, C2×C7×D489, C2×C3×C7×D163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4564, 9);