Finite Group DatabasebetaFinite Group Databasebeta| order | 5652 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×Dic157⋊C3 |
| unambiguous semidirect product | Dic157⋊C32 |
| unambiguous semidirect product | (C3×Dic157)⋊C3 |
| derived, Sylow | C157 ⋊ C32×C4 |
| Hall | C3×C157⋊C3 ⋊ C4 |
| Hall | Dic157 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D157⋊C3 |
| commutator, hypocenter | C157 | C32×C4 |
| Frattini | C2 | C3×D157⋊C3 |
| Fitting, socle | C2×C3×C157 | C2×C3 |
| LCS | G ▷ C157 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×Dic157⋊C3, C3×Dic785⋊C3, C3×#15691171⋊C3 |
| maximal normal subgroup of | C3×C5×Dic157⋊C3 |
| maximal quotient of | C3×C5×Dic157⋊C3, C3×Dic785⋊C3, C3×#15691171⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5652, 20);