Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #450 |
188 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3856 |
Polycyclic presentation:
2^6,241|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^240,d^b=df,g^b=g^2402419 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506369, #44506370, #44506375, … |
| maximal normal subgroup of | #44506369, #44506370, #44506375, … |
| maximal quotient of | #44506399, #44506416, #44506467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 702);