Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×M32 ⋊ C2 |
| Sylow | C13 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D13 |
| commutator, socle | C2×C13 | C22×C8 |
| Fitting | C13×M32 | C2 |
| prime radical | #6127 | C4 |
| cosocle | C8×C13 | C23 |
| hypercenter | M32 | D13 |
| hypocenter | C13 | #504 |
| LCS | G ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^12,c^b=cf160 conjugacy classes — view the full character table.
| maximal subgroup of | #13116670, #13116672, #13116675, … |
| maximal normal subgroup of | #13116670, #13116672, #13116675, … |
| maximal quotient of | #13116434, #13116435, #13116448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 534);