Finite Group DatabasebetaFinite Group Databasebeta| order | 644 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic23 |
| unambiguous semidirect product | C23⋊(C4×C7) |
| derived, Sylow | C23 ⋊ C4×C7 |
| Hall | C7×C23 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D23 |
| commutator, hypocenter | C23 | C4×C7 |
| Frattini | C2 | C7×D23 |
| Fitting, socle, prime radical | C2×C7×C23 | C2 |
| cosocle | C2×C23 | C2×C7 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C7 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 644 |
182 conjugacy classes — view the full character table.
| maximal subgroup of | D7×Dic23, D161⋊C4, #13046228, … |
| maximal normal subgroup of | D7×Dic23, D161⋊C4, #13046228, … |
| maximal quotient of | C7×C23⋊C8, C2×C7×Dic23, C3×C7×Dic23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(644, 2);