Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#16838533 |
| Fitting | C4×D4×C239 ⋊ C2 |
| Sylow | C239 ⋊ C4×D8 |
134 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
2408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483340, C8×#16838533, #44483369, … |
| maximal normal subgroup of | #44483340, C8×#16838533, #44483369, … |
| maximal quotient of | C8×#16838533, #44483375, #44483377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 630);