Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #347 |
46 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4688 |
Polycyclic presentation:
2^6,293|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,c^b=cf,g^b=g^138,g^d=g^2921190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#34037019, #49175000, #49175004, … |
| maximal normal subgroup of | C2×#34037019, #49175000, #49175004, … |
| maximal quotient of | #49173701, #49173704, #49173825, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1439);