Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#261 |
| commutator, socle | C2×C13 | C22×C8 |
| Fitting | C13×M16 | C4 |
| prime radical | #6127 | C4 |
| cosocle | #1055 | C23 |
| hypercenter | M16 | #261 |
| hypocenter | C13 | #504 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C4 ◁ M16 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=d,c^2=e,d^2=e,e^2=f,g^a=g^8,c^b=cf,g^d=g^1270 conjugacy classes — view the full character table.
| maximal subgroup of | #13131224, #13131225, #13131227, … |
| maximal normal subgroup of | #13131224, #13131225, #13131227, … |
| maximal quotient of | #13131046, #13131047, #13131067, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1062);