Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D41 |
| Fitting | C2×C4×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D41 |
| commutator, hypocenter | C41 | C22×C4 |
| Frattini | C2 | C22×D41 |
| Fitting | C2×C4×C41 | C2 |
| socle | C22×C41 | C22 |
| prime radical | C22×D41 | C2 |
| cosocle | C2×C41 | C23 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #13050076, C42×D41, C22⋊C4×D41, … |
| maximal normal subgroup of | #13050076, C42×D41, C22⋊C4×D41, … |
| maximal quotient of | C42×D41, C2×C4×Dic41, C22⋊C4×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 37);