Finite Group DatabasebetaFinite Group Databasebeta| order | 656 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#4223 |
| Fitting | C4×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #4223 |
| commutator, hypocenter | C41 | C42 |
| Frattini | C2 | C2×#4223 |
| Fitting | C4×C41 | C4 |
| socle | C2×C41 | C2×C4 |
| prime radical, cosocle | C2×D41 | C22 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 164 |
56 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#4223, #13050218, #13050228, … |
| maximal normal subgroup of | C8×#4223, #13050218, #13050228, … |
| maximal quotient of | (C2×#4223)⋊C4, C8×#4223, C4×#66493, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(656, 31);