Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C17×#532 ⋊ C2 |
| Sylow | C17 ⋊ #34609 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C23×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C2×C17×#532 | C2 |
| hypercenter | C2×#532 | D17 |
| hypocenter | C17 | #34609 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#532 | |
2782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
Polycyclic presentation:
2^8,17|d^2=h,e^2=f,b^a=bf,c^a=cg,d^a=dh,c^b=ch,i^c=i^16512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 336602);