Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C42×D4×C17 ⋊ C2 |
| Sylow | C17 ⋊ #35027 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Fitting | C42×D4×C17 | C2 |
| prime radical | C2×#10587623 | C22 |
| hypercenter | C42×D4 | D17 |
| hypocenter | C17 | #35027 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ C42×D4 | |
1840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|b^2=g,c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=eh,i^a=i^16,c^b=ch,d^b=dh704 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 342907);