Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic633 |
| unambiguous semidirect product | C3⋊(C3×Dic211) |
| derived | C3×C211 ⋊ C3×C4 |
| Hall | C32×C211 ⋊ C4 |
| Sylow | C211 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D633 |
| commutator, hypocenter | C3×C211 | C3×C4 |
| Frattini | C2 | C3×D633 |
| Fitting, socle | C2×C32×C211 | C2 |
| LCS | G ▷ C3×C211 | |
| UCS | C1 ◁ C2×C3 | |
28 conjugacy classes of subgroups.
1908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C3⋊(Dic211⋊C5), C3×Dic3165, C3×C5×Dic633, … |
| maximal normal subgroup of | C3×C3⋊(Dic211⋊C5), C3×C5×Dic633 |
| maximal quotient of | C3×Dic3165, C3×C5×Dic633, C3×C3⋊(C211⋊AGL(1,𝔽5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 23);