Finite Group DatabasebetaFinite Group Databasebeta| order | 32392 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C4049 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4049 | C8 |
| prime radical | D4049 | C4 |
| cosocle | #30633726 | C2 |
| LCS | G ▷ C4049 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4049 |
Polycyclic presentation:
2^3,4049|a^2=b,b^2=c,d^a=d^3384,d^b=d^884,d^c=d^4048514 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32392, 15);