Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of #66502 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C41 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #66502 |
| commutator, hypocenter | C41 | C16 |
| Fitting, socle, prime radical | C2×C41 | C8 |
| cosocle | #66493 | C2 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^4,41|a^2=b,b^2=c,c^2=d,e^a=e^27,e^b=e^32,e^c=e^4026 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10620295, #13050259, #13050260, … |
| maximal normal subgroup of | C2×#10620295, #13050259, #13050260, … |
| maximal quotient of | #13050254, C2×#10620295, C3×#10620295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 28);