Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C4×C293 ⋊ C2 |
| Sylow | C293 ⋊ #396 |
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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=de,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^2922942 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #396×D293, C2×#34036051, #49162021, … |
| maximal normal subgroup of | #396×D293, C2×#34036051, #49162021, … |
| maximal quotient of | #49157027, #49157029, #49157031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 471);