Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D9×#272 |
| Fitting | C2×C9×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | C9×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D9×C3⋊D3 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C23 |
| Frattini | C32 | C2×D3×C3⋊D3 |
| Fitting | C2×C9×H(3,𝔽3) | C22 |
| socle | C2×C32 | D3×C3⋊D3 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
698 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72221851, C2×#72221864 |
| maximal normal subgroup of | C2×#72221864 |
| maximal quotient of | C2×#72221854 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2709);