Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#66491 |
| derived, Sylow | C41 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D41 |
| commutator, hypocenter | C41 | C2×C8 |
| Frattini | C4 | C2×D41 |
| Fitting | C2×C4×C41 | C2 |
| socle, prime radical | C22×C41 | C4 |
| cosocle | C4×C41 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C8×Dic41, C4×#66491, #13050074, … |
| maximal normal subgroup of | C8×Dic41, C4×#66491, #13050074, … |
| maximal quotient of | C4×#66491, C22⋊#66491, C4⋊#66491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 9);