Finite Group DatabasebetaFinite Group Databasebeta| order | 23532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C37⋊C3×#6157 |
| unambiguous semidirect product | (C37×#6157)⋊C3 |
| Fitting, socle, derived, Hall | C37×C53 ⋊ C3×C4 |
| Hall | C37×#6157 ⋊ C3 |
| Hall | C53×C37⋊C3 ⋊ C4 |
| Sylow | C53 ⋊ C4×C37⋊C3 |
| Sylow | C37 ⋊ C3×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C53 | C3×C4 |
| prime radical | D53×C37⋊C3 | C2 |
| cosocle | C37×D53 | C2×C3 |
| LCS | G ▷ C37×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1961 |
255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23532, 20);