Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#21439918 |
| Fitting | C2×C4⋊C4×C239 ⋊ C2 |
| Sylow | C239 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
2420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44482861, #44482881, #44484263, … |
| maximal normal subgroup of | #44482861, #44482881, #44484263, … |
| maximal quotient of | C2×#29504617, C2×#29504619, C2×C4⋊C4×Dic239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1004);