Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C19×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C19 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^d=g^18121 conjugacy classes — view the full character table.
| maximal subgroup of | #14572980, #14572982, #14572989, … |
| maximal normal subgroup of | #14572980, #14572982, #14572989, … |
| maximal quotient of | #14572149, #14572151, #14572222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1345);