Finite Group DatabasebetaFinite Group Databasebeta| order | 32192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D503 |
| Fitting | M32×C503 ⋊ C2 |
| Sylow | C503 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D503 |
| commutator, socle | C2×C503 | C22×C8 |
| Fitting | M32×C503 | C2 |
| prime radical | C22×D503 | C8 |
| cosocle | C8×C503 | C23 |
| hypercenter | M32 | D503 |
| hypocenter | C503 | C2×M32 |
| LCS | G ▷ C2×C503 ▷ C503 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8048 |
5060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32192, 962);