Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | #595 |
| commutator, hypocenter | C17 | C8×C32 |
| Frattini | C4×C8 | C2×#595 |
| Fitting | C4×C16×C17 | C4 |
| socle, prime radical | C22×C17 | C4×C16 |
| cosocle | C4×#63214 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4×C16 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4352 |
Polycyclic presentation:
2^8,17|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,i^a=i^13,i^b=i^16,i^c=i^16512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1084331);