Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C17 ⋊ C4×#557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D17 |
| commutator | C22×C17 | C24×C4 |
| Fitting | C17×#2370 | C2 |
| socle, prime radical, cosocle | C23×C17 | C25 |
| hypercenter | #2370 | D17 |
| hypocenter | C17 | C4×#557 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #2370 | |
2220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4352 |
Polycyclic presentation:
2^8,17|a^2=h,b^2=f,c^2=g,d^2=fg,e^2=fh,b^a=bf,c^a=cg,d^b=df,i^b=i^16,i^e=i^16500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 329565);