Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #10587739⋊C32 |
| derived, Sylow | C137 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #11764049 |
| commutator, hypocenter | C137 | C4×C32 |
| Frattini | C8 | C2×#11764049 |
| Fitting | C16×C137 | C8 |
| socle | C2×C137 | C4×C16 |
| prime radical | C2×D137 | C2×C16 |
| cosocle | #17984161 | C22 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^127,h^b=h^37,h^c=h^100,h^d=h^136,h^e=h^136400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21594);