Finite Group DatabasebetaFinite Group Databasebeta| order | 7596 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C211 · Schur multiplier (H2) = C3 |
| direct product | C3⋊Dic3×C211 |
| unambiguous semidirect product | C3⋊(Dic3×C211) |
| derived, Sylow | C32 ⋊ C4×C211 |
| Hall | C32×C211 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C211 | C3⋊D3 |
| commutator, hypocenter | C32 | C4×C211 |
| Frattini | C2 | C3⋊D3×C211 |
| Fitting, socle | C2×C32×C211 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C211 | |
36 conjugacy classes of subgroups.
2532 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊Dic3×C211⋊C5, C3⋊Dic15×C211, C5×C3⋊Dic3×C211, … |
| maximal normal subgroup of | C3⋊Dic3×C211⋊C5, C5×C3⋊Dic3×C211 |
| maximal quotient of | C3⋊Dic15×C211, C5×C3⋊Dic3×C211, C3⋊ΓL(1,𝔽16)×C211 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7596, 24);