Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C211 |
| direct product | C24×D3×A4 |
| unambiguous semidirect product | C3⋊(C25×A4) |
| unambiguous semidirect product | (C2×C3)⋊(C24×A4) |
| Fitting, socle | C26×C3 ⋊ C2×C3 |
| derived | C22×C3 ⋊ C25×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D3×A4 |
| commutator, cosocle, hypocenter | C22×C3 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26×C3 | C2×C3 |
| LCS | G ▷ C22×C3 | |
| UCS | C1 ◁ C24 | |
22102 conjugacy classes of subgroups; only the 1323 normal subgroups are shown.
This group has 22102 conjugacy classes of subgroups — too many to draw. Only its 1323 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C22×D3×A42, C22×D3×GL(2,ℤ/4), D3×A4×#120, … |
| maximal normal subgroup of | C22×D3×A42, C22×D3×GL(2,ℤ/4), D3×A4×#120 |
| maximal quotient of | C24×(C3⋊D3)⋊A4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157875);