Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C32 |
| direct product | C22×#92300 |
| Fitting | C22×C32⋊H(3,𝔽3) ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C23×C3 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C23×C3 |
| Frattini | C32 | C22×C3×C3⋊D3 |
| Fitting | C22×C32⋊H(3,𝔽3) | C2 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
1350 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 1350 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#13091120, A4×#92300, D4×#92300, … |
| maximal normal subgroup of | A4×#92300, D4×#92300, C22×#11757730, … |
| maximal quotient of | D4×#92300, C22×#13091119 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2901);