Finite Group DatabasebetaFinite Group Databasebeta| order | 37524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D159⋊D59 |
| unambiguous semidirect product | D177⋊D53 |
| unambiguous semidirect product | D3127⋊D3 |
| Fitting, socle, derived, Hall | C3×C53×C59 ⋊ C22 |
| Hall | C53×C59 ⋊ C2×D3 |
| Hall | C3×C59 ⋊ C2×D53 |
| Hall | C3×C53 ⋊ C2×D59 |
| Sylow | C59 ⋊ D3×D53 |
| Sylow | C53 ⋊ D3×D59 |
| Sylow | C3 ⋊ D53×D59 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C53×C59 | C22 |
| LCS | G ▷ C3×C53×C59 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9381 |
Polycyclic presentation:
2^2,3,53,59|d^a=d^52,e^a=e^58,c^b=c^2,d^b=d^522433 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37524, 20);