Finite Group DatabasebetaFinite Group Databasebeta| order | 38532 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Hall | C132×C19 ⋊ C3×C4 |
| Hall | C19⋊#10621725 ⋊ C3 |
| Hall | C19×#92789 ⋊ C4 |
| Hall | #92789 ⋊ Dic19 |
| Sylow | C132 ⋊ C3×Dic19 |
| Sylow | C19 ⋊ #14523129 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #34064212 |
| commutator, hypocenter | C132×C19 | C3×C4 |
| Fitting, socle, cosocle | C2×C132×C19 | C2×C3 |
| prime radical | C2×C19×#92789 | C2 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2964 |
Polycyclic presentation:
2,3,13^2,19,2|a^2=f,c^a=c^12,d^a=d^12,e^a=e^18,c^b=c^3,d^b=d^91130 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38532, 99);