Finite Group DatabasebetaFinite Group Databasebeta| order | 4564 |
| automorphism | Aut(G) order 2218104 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2282 |
| direct product | C2×D1141 |
| unambiguous semidirect product | (C2×C7)⋊D163 |
| unambiguous semidirect product | (C2×C163)⋊D7 |
| Fitting, socle | C2×C7×C163 ⋊ C2 |
| derived, Hall | C7×C163 ⋊ C22 |
| Sylow | C163 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D163 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1141 |
| commutator, cosocle, hypocenter | C7×C163 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C163 | C2 |
| LCS | G ▷ C7×C163 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2282 |
1144 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20292076, C2×#20292077, C2×ΓL(1,𝔽8)⋊D163, … |
| maximal normal subgroup of | C2×#20292076, C2×#20292077, C2×ΓL(1,𝔽8)⋊D163, … |
| maximal quotient of | D3×D1141, C2×D3423, C2×C3×D1141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4564, 7);