Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #33974 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×#595 |
| commutator, socle | C2×C17 | C23×C16 |
| Fitting | C17×#504 | C4 |
| prime radical | #41×D17 | C8 |
| cosocle | #63214 | C24 |
| hypercenter | #504 | #595 |
| hypocenter | C17 | #33974 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ #504 | |
462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|a^2=e,e^2=f,f^2=g,g^2=h,d^a=dh,i^a=i^13,c^b=ch,i^d=i^16,i^e=i^16296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1114087);