Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #103×C293 ⋊ C2 |
| Sylow | C293 ⋊ #468 |
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 39 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|b^2=d,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^292,c^b=cf,g^b=g^292,g^c=g^2922060 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #468×D293, C2×#34036378, #49168393, … |
| maximal normal subgroup of | #468×D293, C2×#34036378, #49168393, … |
| maximal quotient of | #49158253, #49158260, #49158287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 798);