Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C17×#1589 ⋊ C2 |
| Sylow | C17 ⋊ #19883 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D68 |
| commutator, cosocle | C42×C17 | C24 |
| Frattini | C42 | C23×D17 |
| Fitting | C17×#1589 | C2 |
| socle | C22×C17 | D42 |
| hypercenter | #1589 | D17 |
| hypocenter | C17 | #19883 |
| LCS | G ▷ C42×C17 ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1589 | |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^16,c^b=cg,d^b=de,e^b=eg,i^b=i^16,f^c=fh,e^d=eg,i^d=i^16395 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 160837);