Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#131 ⋊ C2 |
| Sylow | C13 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D52 |
| commutator, cosocle | C4×C13 | C24 |
| Frattini | C4 | C23×D13 |
| Fitting | C13×#131 | C2 |
| socle | C2×C13 | C22×D4 |
| hypercenter | #131 | D13 |
| hypocenter | C13 | #578 |
| LCS | G ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|b^2=f,c^2=f,d^2=ef,e^2=f,d^a=de,e^a=ef,g^a=g^12,c^b=cf142 conjugacy classes — view the full character table.
| maximal subgroup of | #13116798, #13116802, #13116812, … |
| maximal normal subgroup of | #13116798, #13116802, #13116812, … |
| maximal quotient of | #13123370, #13123436, #13123681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1424);