Finite Group DatabasebetaFinite Group Databasebeta| order | 24492 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C157 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽13)×C157 |
| unambiguous semidirect product | #261⋊(C3×C157) |
| Fitting, socle, Hall | C13×C157 ⋊ C3×C4 |
| derived, Sylow | C13 ⋊ C3×C4×C157 |
| Hall | #261×C157 ⋊ C3 |
| Hall | C13⋊C3×C157 ⋊ C4 |
| Hall | #261 ⋊ C3×C157 |
| Hall | C13⋊C3 ⋊ C4×C157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C157 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C3×C4×C157 |
| Frattini | C1 | G |
| Fitting, socle | C13×C157 | C3×C4 |
| prime radical | D13⋊C3×C157 | C2 |
| cosocle | D13 | C2×C3×C157 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C157 | |
24 conjugacy classes of subgroups.
2041 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24492, 45);