Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#10625007 |
| Fitting | C2×M16×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
248 conjugacy classes — view the full character table.
| maximal subgroup of | #15673201, C4×#10625007, #15673206, … |
| maximal normal subgroup of | #15673201, C4×#10625007, #15673206, … |
| maximal quotient of | C2×#13092144, C2×#13092147, #15671777, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 561);