Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #126×D19 |
| Fitting | C19×#126 ⋊ C2 |
| Sylow | C19 ⋊ C2×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×#126 | C2 |
| prime radical | C23×D19 | C22 |
| hypercenter | #126 | D19 |
| hypocenter | C19 | C2×#126 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #126 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#126×D19, D19×#529, D19×#538, … |
| maximal normal subgroup of | C2×#126×D19, D19×#529, D19×#538, … |
| maximal quotient of | D19×#383, D19×#387, D19×#388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1072);