Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D293⋊(C4⋊C8) |
| Sylow | C293 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^138,g^c=g^292,g^e=g^2921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173614, #49173620, #49173649, … |
| maximal normal subgroup of | #49173614, #49173620, #49173649, … |
| maximal quotient of | D293⋊#334, D293⋊#335, #49174333, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1550);