Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C137 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | #10587739 |
| commutator, hypocenter | C137 | C128 |
| Fitting | C32×C137 | C4 |
| socle, prime radical | C2×C137 | C64 |
| cosocle | #22577122 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C32 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
Polycyclic presentation:
2^7,137|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^100,h^b=h^1361216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19325);