Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic1198 |
| Sylow | C599 ⋊ C4×Q8 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19168 |
4804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305620, #50305622, C4×#23751066, … |
| maximal normal subgroup of | #50305620, #50305622, C4×#23751066, … |
| maximal quotient of | C4×C4⋊Dic599, C4×Dic599⋊C4, #50305773, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 112);