Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C128 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C2×C128 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #3633 |
| commutator, hypocenter | C17 | C2×C128 |
| Frattini | C16 | C2×#3633 |
| Fitting | C17×C32 | C8 |
| socle | C2×C17 | C2×C64 |
| prime radical | C2×D17 | C64 |
| cosocle | #11763648 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C32 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,g^2=h,i^a=i^9,i^b=i^16,i^c=i^13,i^d=i^16320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116750);