Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C22⋊C4×D599 |
| Fitting | C22⋊C4×C599 ⋊ C2 |
| Sylow | C599 ⋊ C2×C22⋊C4 |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4792 |
3010 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #99×D599, C2×C22⋊C4×D599, #117×D599, … |
| maximal normal subgroup of | #99×D599, C2×C22⋊C4×D599, #117×D599, … |
| maximal quotient of | #95×D599, #50305737, C22⋊C4×Dic599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 96);