Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #204 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C4×#805 |
| Fitting | C32×C43 ⋊ C2 |
| Sylow | C32 ⋊ C4×#104 |
849 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#10590393, C3×C4×#5077, C4×#10590397, … |
| maximal normal subgroup of | C4×#10590393, C3×C4×#5077, C4×#10590397 |
| maximal quotient of | C3×AGL(1,𝔽5)×#805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17875);