Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#22627703 |
| unambiguous semidirect product | D293⋊#117 |
| Fitting | C22×C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C2×#117 |
330 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
1208 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49174450, #49174453, C2×#34036996, … |
| maximal normal subgroup of | #49174450, #49174453, C2×#34036996, … |
| maximal quotient of | C2×#34037065, C2×C4×C22⋊#11924078, C2×C4×C4⋊#11924078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1612);