Finite Group DatabasebetaFinite Group Databasebeta| order | 23532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #21463226⋊C3 |
| Fitting, socle, derived, Hall | C37×C53 ⋊ C3×C4 |
| Hall | #21463226 ⋊ C3 |
| Hall | C53×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ #6157 |
| Sylow | C53 ⋊ #3866⋊C3 |
| Sylow | C37 ⋊ C3×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C53 | C3×C4 |
| prime radical | C53⋊(D37⋊C3) | C2 |
| cosocle | D1961 | C2×C3 |
| LCS | G ▷ C37×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1961 |
Polycyclic presentation:
2,3,2,37,53|a^2=c,d^a=d^31,e^a=e^23,d^b=d^26,d^c=d^36,e^c=e^52210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23532, 16);