Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D3×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×D3×C22⋊A4 |
| Fitting | C24×C3×C4 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C2×C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D3×C22⋊A4 |
| commutator, hypocenter | C24×C3 | C2×C3×C4 |
| Frattini | C2 | C2×D3×C22⋊A4 |
| Fitting | C24×C3×C4 | C2×C3 |
| socle, cosocle | C25×C3 | C22×C3 |
| prime radical | C2×D3×C22⋊A4 | C2 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C4 | |
3725 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 3725 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×C22⋊A4, C4×D3×#1020, C4×D3×A42, … |
| maximal normal subgroup of | C4×D3×#1020, C4×D3×A42, C4×D3×#120⋊C3 |
| maximal quotient of | C4×D3×#997, D3×AGL(1,𝔽5)×C22⋊A4, C4×C3⋊D3×C22⋊A4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157833);