Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#104 ⋊ C2 |
| Sylow | C19 ⋊ #444 |
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^c=g^18148 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#444, C2×#11926663, #14572533, … |
| maximal normal subgroup of | D19×#444, C2×#11926663, #14572533, … |
| maximal quotient of | #14562444, #14562450, #14562451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 668);