Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22⋊C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ #352 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^138,d^b=de,g^b=g^292,d^c=df,g^d=g^292743 conjugacy classes — view the full character table.
| maximal subgroup of | D293⋊#352, C2×#34037032, #49175037, … |
| maximal normal subgroup of | D293⋊#352, C2×#34037032, #49175037, … |
| maximal quotient of | #49173712, #49173729, #49173766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1452);