Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic1198 |
| Sylow | C599 ⋊ C22×Q8 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19168 |
4804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305794, #50305795, #50305796, … |
| maximal normal subgroup of | #50305794, #50305795, #50305796, … |
| maximal quotient of | C22×Dic599⋊C4, C22×C4⋊Dic599, C2×C4×Dic1198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 186);