Finite Group DatabasebetaFinite Group Databasebeta| order | 608 |
| isoclinism | isoclinic class of Dic38 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D19 |
| Fitting | C22×C4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
164 conjugacy classes — view the full character table.
| maximal subgroup of | (C22⋊D19)⋊C8, C8×C22⋊D19, #11926612, … |
| maximal normal subgroup of | (C22⋊D19)⋊C8, C8×C22⋊D19, #11926612, … |
| maximal quotient of | C4×C22⋊Dic19, C4×(C2×D19)⋊C4, C4×Dic19⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(608, 123);