Finite Group DatabasebetaFinite Group Databasebeta| order | 27348 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊#6157 |
| unambiguous semidirect product | (C43⋊#6157)⋊C3 |
| Fitting, socle, derived, Hall | C43×C53 ⋊ C3×C4 |
| Hall | C43⋊#6157 ⋊ C3 |
| Hall | C53×C43⋊C3 ⋊ C4 |
| Hall | C43⋊C3 ⋊ #6157 |
| Sylow | C53 ⋊ (C43⋊C3)⋊C4 |
| Sylow | C43 ⋊ C3×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C43×C53 | C3×C4 |
| prime radical | D53×C43⋊C3 | C2 |
| cosocle | C43×D53 | C2×C3 |
| LCS | G ▷ C43×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2279 |
Polycyclic presentation:
2,3,2,43,53|a^2=c,d^a=d^42,e^a=e^30,d^b=d^36,e^c=e^52247 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27348, 14);