Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C19 ⋊ C2 |
| Sylow | C19 ⋊ #418 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^18,c^b=cf,d^b=df,g^b=g^18202 conjugacy classes — view the full character table.
| maximal subgroup of | #14563604, #14563606, #14564009, … |
| maximal normal subgroup of | #14563604, #14563606, #14564009, … |
| maximal quotient of | #14562027, #14562053, #14562079, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 555);