Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | D42×C17 ⋊ C4 |
| Sylow | C17 ⋊ #34493 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#595 |
| commutator, socle | C22×C17 | C24×C4 |
| Fitting | D42×C17 | C4 |
| prime radical | D42×D17 | C2 |
| cosocle | C22×D17 | C25 |
| hypercenter | D42 | #595 |
| hypocenter | C17 | #34493 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ D42 | |
3076 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
Polycyclic presentation:
2^8,17|a^2=h,c^2=g,d^2=gh,e^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^4,c^b=cg,d^b=df,i^d=i^13,i^h=i^16176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1114604);