Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#17989805 |
| Sylow | C293 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^138,g^d=g^2921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#17989805, #49173736, #49173737, … |
| maximal normal subgroup of | D4⋊#17989805, #49173736, #49173737, … |
| maximal quotient of | #49173807, #49173814, #49173823, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1469);