Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ #354 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=f,c^2=f,b^a=bc,c^a=ce,e^a=ef,c^b=cf,d^b=def,g^b=g^18,d^c=df112 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#354, C2×#11926338, #14565297, … |
| maximal normal subgroup of | D19×#354, C2×#11926338, #14565297, … |
| maximal quotient of | #14561568, #14561578, #14561634, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 343);