Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C293 ⋊ #568 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=e,e^2=f,d^a=df,g^a=g^138,c^b=cf,g^b=g^292,g^c=g^292,g^e=g^292764 conjugacy classes — view the full character table.
| maximal subgroup of | #49174743, #49174787, #49174789, … |
| maximal normal subgroup of | #49174743, #49174787, #49174789, … |
| maximal quotient of | #49175351, #49175357, #49175372, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1629);