Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#21439930 |
| Fitting | C2×C22⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ C2×#120 |
662 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3824 |
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44484955, #44485000, #44485673, … |
| maximal normal subgroup of | #44484955, #44485000, #44485673, … |
| maximal quotient of | C2×#29504627, C2×#29504646, C2×#29504647, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1036);