Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D13 |
| Fitting | C22×C8×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D13 |
| commutator, hypocenter | C13 | C23×C8 |
| Frattini | C4 | C23×D13 |
| Fitting | C22×C8×C13 | C2 |
| socle | C23×C13 | C2×C4 |
| prime radical | C23×D13 | C4 |
| cosocle | C4×C13 | C24 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#336, #13114531, D13×#340, … |
| maximal normal subgroup of | D13×#336, #13114531, D13×#340, … |
| maximal quotient of | C2×C4×C8×D13, C22×C8×Dic13, C2×D13×C22⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1407);