Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C19×#135 ⋊ C2 |
| Sylow | C19 ⋊ #509 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
Polycyclic presentation:
2^6,19|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^b=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | #14565530, #14565533, #14565581, … |
| maximal normal subgroup of | #14565530, #14565533, #14565581, … |
| maximal quotient of | #14565347, #14565350, #14565424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 984);