Finite Group DatabasebetaFinite Group Databasebeta| order | 29412 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C43 ⋊ C4×C9 |
| Hall | #20301349 ⋊ C4 |
| Hall | Dic817 ⋊ C9 |
| Sylow | C43 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ Dic43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | #19096734 |
| commutator, hypocenter | C19×C43 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C19×C43 | C2×C3 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29412 |
Polycyclic presentation:
2,3,19,43,2,3|a^2=e,b^3=f,c^a=c^18,d^a=d^42,c^b=c^7,d^b=d^6852 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29412, 24);