Finite Group DatabasebetaFinite Group Databasebeta| order | 13674 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(D43⋊C3) |
| unambiguous semidirect product | (C43⋊C3)⋊D53 |
| unambiguous semidirect product | D2279⋊C3 |
| Fitting, socle, derived, Hall | C43×C53 ⋊ C2×C3 |
| Hall | C53×C43⋊C3 ⋊ C2 |
| Hall | D2279 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C53 | C2×C3 |
| LCS | G ▷ C43×C53 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2279 |
Polycyclic presentation:
2,3,43,53|c^a=c^42,d^a=d^52,c^b=c^36455 conjugacy classes — view the full character table.
| maximal subgroup of | D53×D43⋊C3, C2×C53⋊(D43⋊C3) |
| maximal normal subgroup of | D53×D43⋊C3, C2×C53⋊(D43⋊C3) |
| maximal quotient of | (C43⋊C3)⋊Dic53, C2×C53⋊(D43⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13674, 12);