Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C8×C293 ⋊ C4 |
| Sylow | C293 ⋊ H(3,ℤ/4) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,g^a=g^155,d^b=df,g^b=g^138,g^d=g^292,g^e=g^2921190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173755, #49173756, #49173757, … |
| maximal normal subgroup of | #49173755, #49173756, #49173757, … |
| maximal quotient of | #49173608, #49173611, #49173634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1417);