Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C33×(C22⋊C9)⋊C2 |
| derived | C22⋊C9 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | (C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | C22⋊C9 | C2×C33 |
| Frattini | C3 | C33×S4 |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C33 | |
894 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3584);