Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C293 ⋊ #417 |
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^292,c^b=cf,d^b=df2942 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49158739, #49158740, #49158744, … |
| maximal normal subgroup of | #49158739, #49158740, #49158744, … |
| maximal quotient of | #49157172, #49157198, #49157224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 550);