Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic293 |
| Sylow | C293 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
2072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49160634, SD32×Dic293, #49160641, … |
| maximal normal subgroup of | #49160634, SD32×Dic293, #49160641, … |
| maximal quotient of | Q16×#14556873, #49157636, #49157682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 644);