Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C82×C17 ⋊ C4 |
| Sylow | C17 ⋊ #7845 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×#595 |
| commutator, socle | C22×C17 | C43 |
| Fitting | C82×C17 | C4 |
| prime radical | C22×D17 | C2×C42 |
| cosocle | C42×D17 | C23 |
| hypercenter | C82 | #595 |
| hypocenter | C17 | #7845 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C42 ◁ C82 | |
486 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=cgh,c^b=cg,i^c=i^13,i^f=i^16368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1085531);