Finite Group DatabasebetaFinite Group Databasebeta| order | 15252 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D1271 |
| unambiguous semidirect product | (C2×C41)⋊(C3×D31) |
| Fitting, socle | C2×C3×C31×C41 ⋊ C2 |
| derived, Hall | C31×C41 ⋊ C22×C3 |
| Hall | C3×C31×C41 ⋊ C22 |
| Hall | C3×C41 ⋊ C2×D31 |
| Hall | C3×C31 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C3×D31 |
| Sylow | C31 ⋊ C2×C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1271 |
| commutator, cosocle, hypocenter | C31×C41 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C31×C41 | C2 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 ◁ C2×C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7626 |
3822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15252, 38);