Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #546×C137 ⋊ C2 |
| Sylow | C137 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D137 |
| commutator, socle, cosocle | C22×C137 | C25 |
| Fitting | #546×C137 | C2 |
| hypercenter | #546 | D137 |
| hypocenter | C137 | D4×#41 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C22 ◁ #546 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^136,h^e=h^1361750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 17994);