Finite Group DatabasebetaFinite Group Databasebeta| order | 15756 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#19126826 |
| Fitting, socle, Hall | C3×C13×C101 ⋊ C4 |
| derived, Hall | C13×C101 ⋊ C3×C4 |
| Hall | C3×C101 ⋊ #261 |
| Sylow | C101 ⋊ C3×#261 |
| Hall | C3×C13 ⋊ Dic101 |
| Sylow | C13 ⋊ C3×Dic101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19126826 |
| commutator, hypocenter | C13×C101 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C101 | C4 |
| prime radical | C3×D13×C101 | C2 |
| cosocle | D13×C101 | C2×C3 |
| LCS | G ▷ C13×C101 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3939 |
1221 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15756, 28);