Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D239)⋊C8 |
| Fitting | C22⋊C8×C239 ⋊ C2 |
| Sylow | C239 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7648 |
Polycyclic presentation:
2^6,239|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^2382420 conjugacy classes. The character table is too large to display.
| maximal quotient of | #44483340, #44483345, #44483351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 612);