Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D13⋊C32 |
| derived, Sylow | C13 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #261 |
| commutator, hypocenter | C13 | C2×C32 |
| Frattini | C8 | C2×#261 |
| Fitting | C13×C16 | C4 |
| socle | C2×C13 | C2×C16 |
| prime radical | C2×D13 | C16 |
| cosocle | #6090 | C22 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=c,b^2=d,c^2=d,d^2=e,e^2=f,g^a=g^8,g^c=g^12112 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#261, #13129942, #13129985, … |
| maximal normal subgroup of | C32×#261, #13129942, #13129985, … |
| maximal quotient of | #13129941, #13129950, #13129994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 179);