Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of Dic82 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D41 |
| unambiguous semidirect product | C23⋊D41 |
| Fitting | C23×C41 ⋊ C2 |
| Sylow | C41 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D41 |
| commutator, cosocle | C2×C41 | C23 |
| Frattini | C2 | C22×D41 |
| Fitting | C23×C41 | C2 |
| socle | C22×C41 | C22 |
| hypercenter | C23 | D41 |
| hypocenter | C41 | C2×D4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13050078, #13050124, C4×C22⋊D41, … |
| maximal normal subgroup of | #13050078, #13050124, C4×C22⋊D41, … |
| maximal quotient of | C2×#10620281, C2×C22⋊Dic41, C2×#10620279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 45);