Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#10625056 |
| Fitting | C2×C22⋊C4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#124 |
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #15671747, C4×#10625056, #15675938, … |
| maximal normal subgroup of | #15671747, C4×#10625056, #15675938, … |
| maximal quotient of | C2×#13092281, C2×#13092305, C2×#13092306, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1064);