Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C293 ⋊ #329 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,c^2=f,d^2=e,b^a=bc,c^a=ce,g^a=g^292,c^b=cf,d^b=def2063 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156932, #49156933, #49156935, … |
| maximal normal subgroup of | #49156932, #49156933, #49156935, … |
| maximal quotient of | #49156606, #49156611, #49156666, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 289);