Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C211 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic3×C211 |
| unambiguous semidirect product | C3⋊(C3×C4×C211) |
| derived | C3 ⋊ C3×C4×C211 |
| Hall | C32×C211 ⋊ C4 |
| Sylow | C32 ⋊ C4×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C211 | D3 |
| commutator, hypocenter | C3 | C3×C4×C211 |
| Frattini | C2 | C3×D3×C211 |
| Fitting, socle | C2×C32×C211 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C3×C211 | |
28 conjugacy classes of subgroups.
3798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic3×C211⋊C5, C3×Dic15×C211, C3×C5×Dic3×C211, … |
| maximal normal subgroup of | C3×Dic3×C211⋊C5, C3×C5×Dic3×C211 |
| maximal quotient of | C3×Dic15×C211, C3×C5×Dic3×C211, C3×ΓL(1,𝔽16)×C211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 22);