Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | Q82×#595 |
| Fitting | Q82×C17 ⋊ C4 |
| Sylow | C17 ⋊ C4×Q82 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#595 |
| commutator, socle | C22×C17 | C24×C4 |
| Fitting | Q82×C17 | C4 |
| prime radical, cosocle | C22×D17 | C25 |
| hypercenter | Q82 | #595 |
| hypocenter | C17 | C4×Q82 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
2324 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1114281);