Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| isoclinism | isoclinic class of C157⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×C4×C157⋊C3 |
| unambiguous semidirect product | (C4×C157)⋊C32 |
| unambiguous semidirect product | (C3×C4×C157)⋊C3 |
| Fitting | C3×C4×C157 ⋊ C3 |
| derived, Sylow | C157 ⋊ C32×C4 |
| Hall | C4×C157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C4 | C157⋊C3 |
| commutator, hypocenter | C157 | C32×C4 |
| Frattini | C2 | C2×C3×C157⋊C3 |
| Fitting | C3×C4×C157 | C3 |
| socle | C2×C3×C157 | C2×C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C3×C4 | |
36 conjugacy classes of subgroups.
660 conjugacy classes — view the full character table.
| maximal subgroup of | C3×Dic5×C157⋊C3, C3×C4×C5×C157⋊C3, C3×AGL(1,𝔽5)×C157⋊C3 |
| maximal normal subgroup of | C3×C4×C5×C157⋊C3 |
| maximal quotient of | C3×Dic5×C157⋊C3, C3×C4×C5×C157⋊C3, C3×AGL(1,𝔽5)×C157⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 23);