Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#22627539 |
| Sylow | C293 ⋊ C2×#99 |
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
2942 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156903, #49156904, #49156909, … |
| maximal normal subgroup of | #49156903, #49156904, #49156909, … |
| maximal quotient of | C2×#34035853, C2×#34035855, #49157103, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 520);