Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C214 |
| direct product | C22×C3×#1004 |
| Fitting | C23×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C22×H(5,𝔽2) |
13801 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#10596675, C3×#10943957, C3×#10943884, … |
| maximal normal subgroup of | C22×#10596675, C3×#10943957, C3×#10943884, … |
| maximal quotient of | C3×#11703805 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153224);