Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C3×#71532 |
| Fitting | C22×C32×C42 ⋊ C2 |
| Sylow | C32 ⋊ #1896 |
1133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72252310, #72252312, C3×#10686697, … |
| maximal normal subgroup of | #72252310, #72252312, C3×#10686697, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 22176);