Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #137×C293 ⋊ C2 |
| Sylow | C293 ⋊ #578 |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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=f,b^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^292,d^c=df,g^d=g^2921628 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49170555, #49170557, #49170559, … |
| maximal normal subgroup of | #49170555, #49170557, #49170559, … |
| maximal quotient of | #49167316, #49167317, #49167384, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1365);