Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C293 ⋊ C2 |
| Sylow | C293 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,c^b=cf,d^b=df,g^b=g^2924700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D293, C2×#34035912, #49160411, … |
| maximal normal subgroup of | #350×D293, C2×#34035912, #49160411, … |
| maximal quotient of | #49156710, #49156726, #49156741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 332);