Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | D17×#3557 |
| Fitting | C17×#3557 ⋊ C2 |
| Sylow | C17 ⋊ C2×#3557 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D17 |
| commutator, socle, cosocle | C22×C17 | C26 |
| Fitting | C17×#3557 | C2 |
| prime radical | D17×#540 | C2 |
| hypercenter | #3557 | D17 |
| hypocenter | C17 | C2×#3557 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ #3557 | |
6554 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1077010);