Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C19×C4⋊C8 ⋊ C2 |
| Sylow | C19 ⋊ #431 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=e,c^2=d,e^2=f,b^a=bd,g^b=g^18,g^c=g^18220 conjugacy classes — view the full character table.
| maximal subgroup of | #14562014, #14562016, #14562024, … |
| maximal normal subgroup of | #14562014, #14562016, #14562024, … |
| maximal quotient of | #14563379, #14563392, C4⋊C8×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 601);