Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C19 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1216 |
Polycyclic presentation:
2^6,19|a^2=e,b^2=f,c^2=ef,d^2=f,b^a=bd,d^a=df,d^b=df,g^c=g^18154 conjugacy classes — view the full character table.
| maximal subgroup of | C4×Q16×D19, C2×#11926636, #14572403, … |
| maximal normal subgroup of | C4×Q16×D19, C2×#11926636, #14572403, … |
| maximal quotient of | #14562439, #14562482, #14562488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 641);