Finite Group DatabasebetaFinite Group Databasebeta| order | 3488 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#89137 |
| Fitting | D4×C109 ⋊ C4 |
| Sylow | C109 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#89137 |
| commutator, socle | C2×C109 | C22×C4 |
| Fitting | D4×C109 | C4 |
| prime radical | D4×D109 | C2 |
| cosocle | C2×D109 | C23 |
| hypercenter | D4 | #89137 |
| hypocenter | C109 | C4×D4 |
| LCS | G ▷ C2×C109 ▷ C109 | |
| UCS | C1 ◁ C2 ◁ D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 436 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3488, 226);