Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊(C3⋊S4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C34 |
| direct product | C32×C3⋊(C3⋊S4) |
| unambiguous semidirect product | C3⋊(C32×C3⋊S4) |
| unambiguous semidirect product | A4⋊(C32×C3⋊D3) |
| Fitting, socle | C22×C34 ⋊ D3 |
| derived | C32×A4 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | C32×A4 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C22×C34 | D3 |
| LCS | G ▷ C32×A4 | |
| UCS | C1 ◁ C32 | |
3364 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 3364 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×A4⋊#4183, #72259823, #72259969 |
| maximal quotient of | #72259773 |
| automorphism group of | (C22⋊C9)⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3944);