Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
| direct product | D17×#2561 |
| Fitting | C17×#2561 ⋊ C2 |
| Sylow | C17 ⋊ C2×#2561 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Fitting | C17×#2561 | C2 |
| prime radical | C25×D17 | C22 |
| hypercenter | #2561 | D17 |
| hypocenter | C17 | C2×#2561 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #2561 | |
4166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 544 |
380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 339938);