Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊Dic41 |
| Sylow | C41 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D41 |
| commutator | C2×C41 | C2×C4 |
| Fitting, prime radical | C23×C41 | C2 |
| socle, cosocle | C22×C41 | C22 |
| hypercenter | C23 | D41 |
| hypocenter | C41 | C22⋊C4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^4,41|a^2=c,b^a=bd,e^a=e^40170 conjugacy classes — view the full character table.
| maximal subgroup of | #13050078, #13050079, C22⋊C4×D41, … |
| maximal normal subgroup of | #13050078, #13050079, C22⋊C4×D41, … |
| maximal quotient of | #13050071, C22⋊#66491, #13050079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 19);