Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#21439919 |
| Sylow | C239 ⋊ C2×#117 |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7648 |
3848 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44484244, #44484246, C2×#29504528, … |
| maximal normal subgroup of | #44484244, #44484246, C2×#29504528, … |
| maximal quotient of | C2×#29504618, C2×C4×C22⋊Dic239, C2×C4×C4⋊Dic239, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 1005);