Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C19×C4⋊Q8 ⋊ C2 |
| Sylow | C19 ⋊ #497 |
124 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^b=g^18142 conjugacy classes — view the full character table.
| maximal subgroup of | #14562940, #14562945, #14562950, … |
| maximal normal subgroup of | #14562940, #14562945, #14562950, … |
| maximal quotient of | #14563260, #14563267, #14563279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 941);