Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of D33⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×D33⋊C3 |
| unambiguous semidirect product | D33⋊C32 |
| unambiguous semidirect product | (C3×D33)⋊C3 |
| Fitting, socle | C34 ⋊ C2×A4 |
| derived | #1113 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D33⋊C3 |
| commutator, cosocle, hypocenter | #1113 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C34 | C2×A4 |
| LCS | G ▷ #1113 | |
| UCS | C1 ◁ C3 | |
222 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 18 |
51 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3880);