Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D13×C22⋊Q8 |
| Fitting | C13×C22⋊Q8 ⋊ C2 |
| Sylow | C13 ⋊ C2×C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C13×C22⋊Q8 | C2 |
| prime radical | C23×D13 | C22 |
| hypercenter | C22⋊Q8 | D13 |
| hypocenter | C13 | C2×C22⋊Q8 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#328, #13113354, #13113367, … |
| maximal normal subgroup of | D13×#328, #13113354, #13113367, … |
| maximal quotient of | D13×#380, D13×#385, D13×#387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1297);