Finite Group DatabasebetaFinite Group Databasebeta| order | 2144 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C4×D67 |
| Fitting | C22⋊C4×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 536 |
350 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D67, C2×C22⋊C4×D67, #117×D67, … |
| maximal normal subgroup of | #99×D67, C2×C22⋊C4×D67, #117×D67, … |
| maximal quotient of | #95×D67, #16863243, C22⋊C4×Dic67, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2144, 96);