Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C293 ⋊ #341 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^138,g^e=g^292758 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037004, #49174478, #49174559, … |
| maximal normal subgroup of | C2×#34037004, #49174478, #49174559, … |
| maximal quotient of | #49173614, #49173616, #49173618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1424);