Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C293 ⋊ C2 |
| Sylow | C293 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^c=g^2921622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #509×D293, C2×#34036563, #49171917, … |
| maximal normal subgroup of | #509×D293, C2×#34036563, #49171917, … |
| maximal quotient of | #49160494, #49160499, #49160570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 983);