Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C41 ⋊ C2 |
| Sylow | C41 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D41 |
| commutator | C2×C41 | C2×C4 |
| Fitting | C2×C4×C41 | C2 |
| socle, cosocle | C22×C41 | C22 |
| prime radical | C22×D41 | C2 |
| hypercenter | C2×C4 | D41 |
| hypocenter | C41 | C22⋊C4 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^4,41|b^2=c,b^a=bd,e^a=e^40170 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D41, C2×#10620281, #13050121, … |
| maximal normal subgroup of | C22⋊C4×D41, C2×#10620281, #13050121, … |
| maximal quotient of | #13050071, #13050076, #13050078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 14);