Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #578 |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^d=g^18148 conjugacy classes — view the full character table.
| maximal subgroup of | #14565598, #14565602, #14565612, … |
| maximal normal subgroup of | #14565598, #14565602, #14565612, … |
| maximal quotient of | #14572163, #14572231, #14572472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1362);