Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Sylow | C17 ⋊ #14714 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D17 |
| commutator | C23×C17 | C23×C4 |
| Fitting | C17×C4⋊#95 | C2 |
| socle, prime radical, cosocle | C24×C17 | C24 |
| hypercenter | C4⋊#95 | D17 |
| hypocenter | C17 | #14714 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C4⋊#95 | |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4352 |
Polycyclic presentation:
2^8,17|a^2=h,b^2=efh,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,i^c=i^16536 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 100937);