Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C4 · Schur multiplier (H2) = C221 |
| direct product | C26×#595 |
| unambiguous semidirect product | D17⋊(C25×C4) |
| Fitting, socle | C26×C17 ⋊ C4 |
| derived, Sylow | C17 ⋊ C26×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C26 | #595 |
| commutator, hypocenter | C17 | C26×C4 |
| Frattini | C1 | G |
| Fitting, socle | C26×C17 | C4 |
| prime radical | C26×D17 | C2 |
| cosocle | D17 | C27 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C26 | |
111198 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116308);