Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22⋊Q8×C241 ⋊ C2 |
| Sylow | C241 ⋊ #543 |
242 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 103 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,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,g^d=g^2401702 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44506366, #44506369, #44506400, … |
| maximal normal subgroup of | #44506366, #44506369, #44506400, … |
| maximal quotient of | #44510056, #44510058 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1174);