Finite Group DatabasebetaFinite Group Databasebeta| order | 832 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D13 |
| commutator, socle, prime radical, cosocle | C23×C13 | C23 |
| Fitting | C22×Q8×C13 | C2 |
| hypercenter | C22×Q8 | D13 |
| hypocenter | C13 | #395 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^6,13|a^2=f,b^2=f,c^2=f,b^a=be,c^a=cd,g^a=g^12,c^b=cf142 conjugacy classes — view the full character table.
| maximal subgroup of | #13113796, #13113798, #13113803, … |
| maximal normal subgroup of | #13113796, #13113798, #13113803, … |
| maximal quotient of | #13113086, #13113099, #13113107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(832, 856);