Finite Group DatabasebetaFinite Group Databasebeta| order | 664 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic83 |
| unambiguous semidirect product | (C2×C83)⋊C4 |
| derived, Sylow | C83 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D83 |
| commutator, hypocenter | C83 | C2×C4 |
| Frattini | C2 | C2×D83 |
| Fitting, socle, prime radical | C22×C83 | C2 |
| cosocle | C2×C83 | C22 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C22 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 664 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Dic83, (C2×D83)⋊C4, C22⋊Dic83, … |
| maximal normal subgroup of | C4×Dic83, (C2×D83)⋊C4, C22⋊Dic83, … |
| maximal quotient of | C4×Dic83, C22⋊Dic83, C4⋊Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(664, 6);