Finite Group DatabasebetaFinite Group Databasebeta| order | 3488 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C109 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #89137 |
| commutator, hypocenter | C109 | C32 |
| Fitting | C8×C109 | C4 |
| socle, prime radical | C2×C109 | C16 |
| cosocle | #13182004 | C2 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 3488 |
Polycyclic presentation:
2^5,109|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^33,f^b=f^108248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3488, 196);