Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #563 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D13 |
| commutator, socle, cosocle | C22×C13 | C24 |
| Fitting | C13×#124 | C2 |
| prime radical | C2×D4×C13 | C22 |
| hypercenter | #124 | D13 |
| hypocenter | C13 | #563 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ #124 | |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=f,c^2=f,d^2=f,c^a=cf,d^a=def,g^a=g^12,c^b=ce,d^b=df,d^c=df103 conjugacy classes — view the full character table.
| maximal subgroup of | #13114132, #13114135, #13114145, … |
| maximal normal subgroup of | #13114132, #13114135, #13114145, … |
| maximal quotient of | #13117986, #13117996, #13118010, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1343);