Finite Group DatabasebetaFinite Group Databasebeta| order | 15540 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×#11715912 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C37 | C3×C4 |
| prime radical | D5×#11715912 | C2 |
| cosocle | C7×D5×C37 | C2×C3 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1295 |
445 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15540, 88);