Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #339 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2344 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^155,g^b=g^138,g^d=g^292,g^e=g^292758 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037001, #49174467, #104×#11924078, … |
| maximal normal subgroup of | C2×#34037001, #49174467, #104×#11924078, … |
| maximal quotient of | #49173612, #49173618, #49173619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1421);