Finite Group DatabasebetaFinite Group Databasebeta| order | 15588 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C4×#16838985 |
| derived, Sylow | C433 ⋊ C4×C9 |
| Hall | C4×C433 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C433⋊C3 |
| commutator, hypocenter | C433 | C4×C9 |
| Frattini | C2×C3 | C2×C433⋊C3 |
| Fitting | C3×C4×C433 | C3 |
| socle, prime radical, cosocle | C2×C3×C433 | C2×C3 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C3×C4 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15588 |
1764 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15588, 3);