Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of D41 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D41 |
| unambiguous semidirect product | C41⋊C24 |
| unambiguous semidirect product | (C2×C41)⋊C23 |
| Fitting, socle | C23×C41 ⋊ C2 |
| derived, Sylow | C41 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D41 |
| commutator, cosocle, hypocenter | C41 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C41 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D41, C2×#10620281, #13050132, … |
| maximal normal subgroup of | C22⋊C4×D41, C2×#10620281, #13050132, … |
| maximal quotient of | C22×C4×D41, C23×Dic41, C2×D4×D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 52);