Finite Group DatabasebetaFinite Group Databasebeta| order | 37524 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3127 |
| unambiguous semidirect product | C59⋊(C3×Dic53) |
| derived, Hall | C53×C59 ⋊ C3×C4 |
| Hall | C3×C53×C59 ⋊ C4 |
| Hall | C3×C59 ⋊ Dic53 |
| Hall | C3×C53 ⋊ Dic59 |
| Sylow | C59 ⋊ C3×Dic53 |
| Sylow | C53 ⋊ C3×Dic59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3127 |
| commutator, hypocenter | C53×C59 | C3×C4 |
| Frattini | C2 | C3×D3127 |
| Fitting, socle, prime radical | C2×C3×C53×C59 | C2 |
| cosocle | C2×C53×C59 | C2×C3 |
| LCS | G ▷ C53×C59 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37524 |
9390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37524, 4);