Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Q8×D41 |
| Fitting | Q8×C41 ⋊ C2 |
| Sylow | C41 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D41 |
| commutator, socle, cosocle | C2×C41 | C23 |
| Fitting | Q8×C41 | C2 |
| prime radical | C2×D41 | C22 |
| hypercenter | Q8 | D41 |
| hypocenter | C41 | C2×Q8 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 328 |
110 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×D41, Q16×D41, #13050193, … |
| maximal normal subgroup of | SD16×D41, Q16×D41, #13050193, … |
| maximal quotient of | C4⋊C4×D41, #13050129, Q8×Dic41, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 42);