Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×Q8×C19 ⋊ C2 |
| Sylow | C19 ⋊ #460 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=d,c^2=f,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^18,e^c=ef199 conjugacy classes — view the full character table.
| maximal subgroup of | #14562694, #14562696, #14562700, … |
| maximal normal subgroup of | #14562694, #14562696, #14562700, … |
| maximal quotient of | #14562983, #14562995, #14563005, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 749);