Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic3×#997 |
| unambiguous semidirect product | C3⋊(C4×#997) |
| derived | C3×H(5,𝔽2) ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | D3×C22⋊A4 |
| commutator, hypocenter | C3×H(5,𝔽2) | C3×C4 |
| Fitting, cosocle | C2×C3×H(5,𝔽2) | C2×C3 |
| socle | C22×C3 | C2×C22⋊A4 |
| prime radical | C2×C3×#997 | C2 |
| LCS | G ▷ C3×H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
716 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽16)×#997, C4×D3×#997, Dic3×#5935, … |
| maximal normal subgroup of | C4×D3×#997, Dic3×#5935, #72231155, … |
| maximal quotient of | ΓL(1,𝔽16)×#997 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157445);