Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C128 · Schur multiplier (H2) = C2 |
| direct product | C2×#14545782 |
| derived, Sylow | C17 ⋊ C2×C128 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #3633 |
| commutator, hypocenter | C17 | C2×C128 |
| Frattini | C16 | C2×#3633 |
| Fitting | C2×C16×C17 | C8 |
| socle, prime radical | C22×C17 | C64 |
| cosocle | #11763648 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C2×C16 | |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4352 |
320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1116749);