Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of AGL(1,𝔽17) |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽17) |
| commutator, hypocenter | C17 | C32 |
| Fitting, socle, prime radical | C2×C17 | C16 |
| cosocle | #63241 | C2 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^5,17|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^3,f^b=f^9,f^c=f^13,f^d=f^1634 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10587664, #11763938, #11763939, … |
| maximal normal subgroup of | C2×#10587664, #11763938, #11763939, … |
| maximal quotient of | #11763933, C2×#10587664, C3×#10587664, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 200);