Finite Group DatabasebetaFinite Group Databasebeta| order | 3488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C109 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#89137 |
| commutator, socle | C2×C109 | C2×C8 |
| Fitting | C8×C109 | C4 |
| prime radical | C2×D109 | C8 |
| cosocle | #11724784 | C22 |
| hypercenter | C8 | #89137 |
| hypocenter | C109 | M32 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C4 ◁ C8 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1744 |
Polycyclic presentation:
2^5,109|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^33,f^b=f^108,f^c=f^108236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3488, 221);