Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #121×D19 |
| Fitting | C19×#121 ⋊ C2 |
| Sylow | C19 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D19 |
| commutator, socle, cosocle | C22×C19 | C24 |
| Fitting | C19×#121 | C2 |
| hypercenter | #121 | D19 |
| hypocenter | C19 | C2×#121 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C22 ◁ #121 | |
426 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 304 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#327, #14562149, #14562162, … |
| maximal normal subgroup of | D19×#327, #14562149, #14562162, … |
| maximal quotient of | D19×#380, D19×#386, D19×#388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1037);