Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#17989791 |
| Fitting | C22×C8×C293 ⋊ C2 |
| Sylow | C293 ⋊ C22×SD16 |
298 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
4700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49159118, #49159120, #49159139, … |
| maximal normal subgroup of | #49159118, #49159120, #49159139, … |
| maximal quotient of | C22×#22627546, C22×#22627549, C22×#22627556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 1323);