Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ #459 |
140 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
Polycyclic presentation:
2^6,19|b^2=d,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 | #14562689, #14562691, #14562700, … |
| maximal normal subgroup of | #14562689, #14562691, #14562700, … |
| maximal quotient of | #14562976, #14562990, #14563000, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 744);