Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| 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,c^b=cf,g^b=g^18328 conjugacy classes — view the full character table.
| maximal subgroup of | #14561720, #14561722, #14561723, … |
| maximal normal subgroup of | #14561720, #14561722, #14561723, … |
| maximal quotient of | C8×#64520, #14561918, #14561924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 504);