Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#22627553 |
| Sylow | C293 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18752 |
4712 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49156724, #49158633, C4×#22627553, … |
| maximal normal subgroup of | #49156724, #49158633, C4×#22627553, … |
| maximal quotient of | C2×#34035879, C2×#34035881, #49157531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 569);