Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C27 |
| direct product | C3×C4×#953 |
| Fitting | C24×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C4×#120 |
3129 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#63694⋊C3, C3×C4×C3⋊#1020, C4×#11724050, … |
| maximal normal subgroup of | C3×C4×#5032, C4×#10595527, C4×#10591725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 35990);