Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | C3×#6292⋊C3 |
| unambiguous semidirect product | #6292⋊C32 |
| unambiguous semidirect product | (C3×#6292)⋊C3 |
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D3×(C3⋊D3)⋊C3 |
| commutator, cosocle | C2×C33 | C22×C32 |
| Frattini | C2×C3 | C32×D32 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3×D3 |
| hypocenter | C33 | C32×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2×C3 | |
761 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 761 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | #72229124, C3×#67×(C3⋊D3)⋊C3, C3×#89039⋊C3, … |
| maximal normal subgroup of | C3×#67×(C3⋊D3)⋊C3, C3×#89039⋊C3, C3×#13048340 |
| maximal quotient of | #72229124 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3014);