Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C64 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C13 ⋊ C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #261 |
| commutator, hypocenter | C13 | C64 |
| Fitting | C13×C16 | C4 |
| socle, prime radical | C2×C13 | C32 |
| cosocle | #88034 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C16 | |
14 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^6,13|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,g^a=g^8,g^b=g^12112 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11718037, D13⋊C64, #13130005, … |
| maximal normal subgroup of | C2×#11718037, D13⋊C64, #13130005, … |
| maximal quotient of | #13129651, C2×#11718037 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 3);