Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#22627684 |
| Sylow | C293 ⋊ C2×#100 |
186 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49173869, #49173870, C4×#22627684, … |
| maximal normal subgroup of | #49173869, #49173870, C4×#22627684, … |
| maximal quotient of | C2×#34036972, C2×#34036973, #49174024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1531);