Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C293 ⋊ C2 |
| Sylow | C293 ⋊ #576 |
268 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|e^2=f,b^a=be,e^a=ef,g^a=g^292,e^b=ef,g^b=g^292,d^c=df2942 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49160740, #49160744, #49160754, … |
| maximal normal subgroup of | #49160740, #49160744, #49160754, … |
| maximal quotient of | #49167312, #49167385, #49167619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1354);