Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8 |
| direct product | M32×#3633 |
| Fitting | C17×M32 ⋊ C8 |
| Sylow | C17 ⋊ C8×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#3633 |
| commutator, socle | C2×C17 | C2×C82 |
| Fitting | C17×M32 | C8 |
| prime radical | C22×D17 | C4×C8 |
| cosocle | C8×#595 | C23 |
| hypercenter | M32 | #3633 |
| hypocenter | C17 | C8×M32 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C8 ◁ M32 | |
354 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 272 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1117062);