Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C293 ⋊ C4 |
| Sylow | C293 ⋊ #440 |
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2344 |
Polycyclic presentation:
2^6,293|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^155,d^b=df,g^c=g^138,g^e=g^292533 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#34037168, #49175539, AGL(1,ℤ/8)×#11924078, … |
| maximal normal subgroup of | C2×#34037168, #49175539, AGL(1,ℤ/8)×#11924078, … |
| maximal quotient of | SD16⋊#14556880, #49174375, #49174376, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1588);