Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#10625064 |
| Fitting | C2×C4⋊C4×C23 ⋊ C2 |
| Sylow | C23 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15671714, #15671734, #15673188, … |
| maximal normal subgroup of | #15671714, #15671734, #15673188, … |
| maximal quotient of | C2×#13092264, C2×C4⋊C4×Dic23, C4×#10625064, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1009);