Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C17 ⋊ #33432 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×#595 |
| commutator, socle | C22×C17 | C23×C8 |
| Fitting, prime radical | C17×#525 | C4 |
| cosocle | C2×#3622 | C24 |
| hypercenter | #525 | #595 |
| hypocenter | C17 | #33432 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|a^2=f,c^2=f,f^2=g,g^2=h,b^a=be,d^a=dh,i^a=i^13,i^c=i^13,i^f=i^16224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1113780);