Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C2×C17×#529 ⋊ C2 |
| Sylow | C17 ⋊ #62755 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D17 |
| commutator, socle, cosocle | C22×C17 | C26 |
| Frattini | C22 | C25×D17 |
| Fitting | C2×C17×#529 | C2 |
| hypercenter | C2×#529 | D17 |
| hypocenter | C17 | #62755 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#529 | |
6644 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|c^2=h,d^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dg,e^a=eh,i^a=i^16,c^b=cg,d^b=dh524 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1077354);