Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | D13×M32 |
| Fitting | C13×M32 ⋊ C2 |
| Sylow | C13 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D13 |
| commutator, socle | C2×C13 | C22×C8 |
| Fitting | C13×M32 | C2 |
| prime radical | C22×D13 | C8 |
| cosocle | C8×C13 | C23 |
| hypercenter | M32 | D13 |
| hypocenter | C13 | C2×M32 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#347, #13116439, D13×#349, … |
| maximal normal subgroup of | D13×#347, #13116439, D13×#349, … |
| maximal quotient of | D13×#346, M32×Dic13, #13116429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 533);