Finite Group DatabasebetaFinite Group Databasebeta| order | 1368 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C19 ⋊ C2×C9 |
| Hall | #4296 ⋊ D4 |
| Hall | C22⋊D19 ⋊ C9 |
| Sylow | C19 ⋊ D4×C9 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 76 |
Polycyclic presentation:
2^2,3,2,3,19|c^3=e,b^a=bd,f^a=f^18,f^c=f^4,f^e=f^749 conjugacy classes — view the full character table.
| maximal subgroup of | D4×AGL(1,𝔽19), #72220613, #72227350, … |
| maximal normal subgroup of | D4×AGL(1,𝔽19), C2×#13062971, #72241735, … |
| maximal quotient of | #72227350, #72227353, C2×#13062971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1368, 71);