Finite Group DatabasebetaFinite Group Databasebeta| order | 32192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #123×D503 |
| Fitting | #123×C503 ⋊ C2 |
| Sylow | C503 ⋊ C2×#123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D503 |
| commutator, socle, cosocle | C22×C503 | C24 |
| Fitting | #123×C503 | C2 |
| prime radical | C2×D4×D503 | C2 |
| hypercenter | #123 | D503 |
| hypocenter | C503 | C2×#123 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ #123 | |
342 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8048 |
3542 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32192, 1049);