Finite Group DatabasebetaFinite Group Databasebeta| order | 15424 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C241 ⋊ #533 |
222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 7712 |
Polycyclic presentation:
2^6,241|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,g^d=g^2401708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44505942, #44505955, #44505994, … |
| maximal normal subgroup of | #44505942, #44505955, #44505994, … |
| maximal quotient of | #44509847, #44509916, #44509918, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15424, 1101);