Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C19 ⋊ C3×C4 |
| Hall | C19×#10621730 ⋊ C3 |
| Hall | C13×#10625202 ⋊ C4 |
| Hall | #10621730 ⋊ C19⋊C3 |
| Sylow | C132 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ #14523157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C132×C19 | C3×C4 |
| prime radical | D13×#10625202 | C2 |
| cosocle | C13×C19×D13 | C2×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2964 |
Polycyclic presentation:
2,3,2,13^2,19|a^2=c,d^a=d^5,e^a=e^12,e^b=e^3,f^b=f^7,d^c=d^12367 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 214);