Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #346 |
54 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=bf,g^b=g^138,g^d=g^2921208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173894, #49173895, C2×#34037016, … |
| maximal normal subgroup of | #49173894, #49173895, C2×#34037016, … |
| maximal quotient of | #49173696, #14556880⋊C16, (C2×#11924078)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1436);