Finite Group DatabasebetaFinite Group Databasebeta| order | 624 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×AGL(1,𝔽13) |
| unambiguous semidirect product | #261⋊(C22×C3) |
| unambiguous semidirect product | (D13⋊C3)⋊(C2×C4) |
| Fitting, socle | C22×C13 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C22×C3×C4 |
| Hall | C22×#261 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C22×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C22×C13 | C3×C4 |
| prime radical | C22×D13⋊C3 | C2 |
| cosocle | D13 | C23×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C22 | |
108 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, 239);