Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #102×C293 ⋊ C2 |
| Sylow | C293 ⋊ #460 |
128 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 41 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,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^b=g^292,e^c=ef,g^c=g^2922063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #460×D293, C2×#34036328, #49168237, … |
| maximal normal subgroup of | #460×D293, C2×#34036328, #49168237, … |
| maximal quotient of | #49158132, #49158136, #49158144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 748);