Finite Group DatabasebetaFinite Group Databasebeta| order | 15296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×D4×C239 ⋊ C2 |
| Sylow | C239 ⋊ #447 |
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3824 |
Polycyclic presentation:
2^6,239|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^238,d^b=df2399 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44483464, #44483465, #44483475, … |
| maximal normal subgroup of | #44483464, #44483465, #44483475, … |
| maximal quotient of | #44483466, #44483483, #44483534, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15296, 683);