Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C41 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #4223 |
| commutator, hypocenter | C41 | C2×C8 |
| Frattini | C2 | C2×#4223 |
| Fitting | C4×C41 | C4 |
| socle | C2×C41 | C2×C4 |
| prime radical | C2×D41 | C4 |
| cosocle | Dic41 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^4,41|a^2=c,b^2=d,c^2=d,e^a=e^32,e^c=e^4056 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#4223, #13050218, #13050226, … |
| maximal normal subgroup of | C8×#4223, #13050218, #13050226, … |
| maximal quotient of | C4×#66493, #13050221, #13050231, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 29);