Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic19⋊C8 |
| Sylow | C19 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^5,19|a^2=d,b^2=c,c^2=e,b^a=bd,f^a=f^18164 conjugacy classes — view the full character table.
| maximal subgroup of | C4⋊C8×D19, C2×Dic19⋊C8, #11926566, … |
| maximal normal subgroup of | C4⋊C8×D19, C2×Dic19⋊C8, #11926566, … |
| maximal quotient of | #11926294, #11926296, #11926298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 20);