Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C17 ⋊ #33480 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3633 |
| commutator, socle | C22×C17 | C23×C8 |
| Fitting, prime radical | C17×#121 | C8 |
| cosocle | C2×#3624 | C24 |
| hypercenter | #121 | #3633 |
| hypocenter | C17 | #33480 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #121 | |
526 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|a^2=f,c^2=f,d^2=e,f^2=g,g^2=h,b^a=be,d^a=dh,i^a=i^9,i^c=i^9,i^d=i^16,i^f=i^13,i^g=i^16140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1118463);