Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D293⋊#131 |
| Sylow | C293 ⋊ C2×#131 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=e,e^2=f,g^a=g^138,c^b=cf,g^d=g^292,g^e=g^292770 conjugacy classes — view the full character table.
| maximal subgroup of | #49174561, #49174565, #49174824, … |
| maximal normal subgroup of | #49174561, #49174565, #49174824, … |
| maximal quotient of | #49175345, C4×#22627711, C4×#22627712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1625);