Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C13 ⋊ #432 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#261 |
| commutator, socle | C22×C13 | C22×C4 |
| Fitting | C42×C13 | C4 |
| prime radical | C22×D13 | C2×C4 |
| cosocle | C2×Dic13 | C23 |
| hypercenter | C42 | #261 |
| hypocenter | C13 | #432 |
| LCS | G ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C42 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^6,13|a^2=d,b^2=ef,c^2=e,d^2=f,b^a=be,c^a=cf,g^a=g^8,g^d=g^1276 conjugacy classes — view the full character table.
| maximal subgroup of | #13129686, #13129692, #13129696, … |
| maximal normal subgroup of | #13129686, #13129692, #13129696, … |
| maximal quotient of | #13130553, #13130563, #13130621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 1021);