Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C19×#97 ⋊ C2 |
| Sylow | C19 ⋊ #405 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=d,b^2=e,d^2=f,g^a=g^18,c^b=cf,g^c=g^18220 conjugacy classes — view the full character table.
| maximal subgroup of | #14565238, #14565449, D19×#405, … |
| maximal normal subgroup of | #14565238, #14565449, D19×#405, … |
| maximal quotient of | #14561914, #14561920, #14561921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 506);