Finite Group DatabasebetaFinite Group Databasebeta| order | 664 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D83 |
| Fitting | C4×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D83 |
| commutator, hypocenter | C83 | C2×C4 |
| Frattini | C2 | C2×D83 |
| Fitting | C4×C83 | C2 |
| socle, cosocle | C2×C83 | C22 |
| prime radical | C2×D83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 332 |
172 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D83, #13050573, C2×C4×D83, … |
| maximal normal subgroup of | C8×D83, #13050573, C2×C4×D83, … |
| maximal quotient of | C4×Dic83, (C2×D83)⋊C4, Dic83⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(664, 4);