Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C42×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^138,g^d=g^2921196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34037000, #49174466, #104×#11924078, … |
| maximal normal subgroup of | C2×#34037000, #49174466, #104×#11924078, … |
| maximal quotient of | #49173613, #49173617, #49173620, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1420);