Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of Dic26 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic26 |
| Sylow | C13 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D13 |
| commutator, cosocle | C2×C13 | C25 |
| Frattini | C2 | C24×D13 |
| Fitting | C23×C4×C13 | C2 |
| socle, prime radical | C24×C13 | C22 |
| hypercenter | C23×C4 | D13 |
| hypocenter | C13 | C23×Q8 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
232 conjugacy classes — view the full character table.
| maximal subgroup of | #13113106, #13114759, #13114770, … |
| maximal normal subgroup of | #13113106, #13114759, #13114770, … |
| maximal quotient of | C23×#6101, C23×C4⋊Dic13, C22×C4×Dic26, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1601);