Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C17×#387 ⋊ C4 |
| Sylow | C17 ⋊ #14704 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#595 |
| commutator, socle | C23×C17 | C23×C4 |
| Fitting | C17×#387 | C4 |
| prime radical, cosocle | C23×D17 | C24 |
| hypercenter | #387 | #595 |
| hypocenter | C17 | #14704 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #387 | |
1422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^8,17|a^2=h,b^2=fh,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=dg,i^a=i^4,i^b=i^13,i^h=i^16200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1099199);