Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215×C3 |
| direct product | C24×C4×C3⋊D3 |
| Fitting | C24×C32×C4 ⋊ C2 |
| derived, Sylow | C32 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | C3⋊D3 |
| commutator, hypocenter | C32 | C25×C4 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C24×C32×C4 | C2 |
| socle | C25×C32 | C22 |
| prime radical | C25×C3⋊D3 | C2 |
| cosocle | C2×C32 | C26 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24×C4 | |
31656 conjugacy classes of subgroups; only the 8681 normal subgroups are shown.
This group has 31656 conjugacy classes of subgroups — too many to draw. Only its 8681 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
384 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C3⋊D3×AGL(1,𝔽5), C4×C3⋊D3×#120, C4×#10595527, … |
| maximal normal subgroup of | C4×C3⋊D3×#120, C4×#10595527, C4×C3⋊D3×C22⋊A4, … |
| maximal quotient of | C24×C3⋊D3×AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153157);