Finite Group DatabasebetaFinite Group Databasebeta| order | 19168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic599⋊C4 |
| Sylow | C599 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19168 |
4804 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #50305615, #50305741, C4×Dic599⋊C4, … |
| maximal normal subgroup of | #50305615, #50305741, C4×Dic599⋊C4, … |
| maximal quotient of | C2×C599⋊#95, C4×Dic599⋊C4, #50305748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19168, 100);