Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of AGL(1,𝔽17) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×AGL(1,𝔽17) |
| Fitting, socle | C2×C17 ⋊ C16 |
| derived, Sylow | C17 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽17) |
| commutator, hypocenter | C17 | C2×C16 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17 | C16 |
| prime radical | C2×D17 | C8 |
| cosocle | #3633 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34 |
34 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 242);