Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C4×AGL(1,𝔽13) |
| unambiguous semidirect product | #261⋊(C3×C4) |
| unambiguous semidirect product | (C4×#261)⋊C3 |
| Fitting | C4×C13 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C3×C42 |
| Hall | C4×#261 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C3×C42 |
| Frattini | C2 | C2×AGL(1,𝔽13) |
| Fitting | C4×C13 | C3×C4 |
| socle | C2×C13 | C2×C3×C4 |
| prime radical | C2×D13⋊C3 | C22 |
| cosocle | C2×D13 | C22×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C4 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 52 |
52 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(624, 119);