Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C19×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C19 ⋊ #453 |
168 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 152 |
Polycyclic presentation:
2^6,19|d^2=f,b^a=bd,c^a=ce,d^a=df,d^b=df,e^b=ef,d^c=df,g^c=g^18115 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#453, C2×#11926710, #14572981, … |
| maximal normal subgroup of | D19×#453, C2×#11926710, #14572981, … |
| maximal quotient of | #14562551, #14562556, #14562578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 715);