Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #365 |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^155,d^b=df,g^d=g^2921184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34037054, D293⋊#365, #49175132, … |
| maximal normal subgroup of | C2×#34037054, D293⋊#365, #49175132, … |
| maximal quotient of | #49173810, #49173811, #49173850, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1474);