Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4⋊C4×#11924078 |
| Fitting | C4⋊C4×C293 ⋊ C4 |
| Sylow | C293 ⋊ C4×C4⋊C4 |
194 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4688 |
770 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #102×#11924078, #103×#11924078, #49174556, … |
| maximal normal subgroup of | #102×#11924078, #103×#11924078, #49174556, … |
| maximal quotient of | #95×#11924078, #49173960, #49173962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1489);