Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C41 ⋊ C2 |
| Sylow | C41 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D41 |
| commutator, socle, cosocle | C2×C41 | C23 |
| Frattini | C2 | C22×D41 |
| Fitting | C2×C4×C41 | C2 |
| hypercenter | C2×C4 | D41 |
| hypocenter | C41 | #41 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
Polycyclic presentation:
2^4,41|b^2=d,c^a=cd,e^a=e^40170 conjugacy classes — view the full character table.
| maximal subgroup of | #13050090, #13050092, #13050170, … |
| maximal normal subgroup of | #13050090, #13050092, #13050170, … |
| maximal quotient of | #13050121, #13050123, C4×C22⋊D41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 39);