Finite Group DatabasebetaFinite Group Databasebeta| order | 3232 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C101 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #87938 |
| commutator, hypocenter | C101 | C32 |
| Fitting | C8×C101 | C4 |
| socle, prime radical | C2×C101 | C16 |
| cosocle | #13108049 | C2 |
| LCS | G ▷ C101 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
Polycyclic presentation:
2^5,101|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^10,f^b=f^100232 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3232, 196);