Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×Q16×C293 ⋊ C2 |
| Sylow | C293 ⋊ #495 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|b^2=d,c^2=ef,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^292,g^b=g^292,g^c=g^2922066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49160842, #49160843, #49160849, … |
| maximal normal subgroup of | #49160842, #49160843, #49160849, … |
| maximal quotient of | #49158378, #49158379, #49158388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 934);