Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C293 ⋊ C2 |
| Sylow | C293 ⋊ #390 |
258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=f,b^2=df,c^2=e,b^a=bd,c^a=ce,g^b=g^2922948 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156716, #49158737, #49158993, … |
| maximal normal subgroup of | #49156716, #49158737, #49158993, … |
| maximal quotient of | #49157014, #49157021, #49157025, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 450);