Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #66419⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#66419⋊C2 |
| Fitting, Sylow | C3×#737 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #66419⋊C2 |
| commutator, cosocle | #4208 | C22×C3 |
| Frattini | C3 | C3×#157⋊D3 |
| Fitting | C3×#737 | D4 |
| socle | C32 | #157⋊D3 |
| hypocenter | #737 | C3×D4 |
| LCS | G ▷ #4208 ▷ #737 | |
| UCS | C1 ◁ C3 | |
213 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3514);