Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #92159 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C22×#92159 |
| Fitting | C22×#6856 ⋊ C2 |
| derived | C3×H(3,𝔽3) ⋊ C23×C3 |
| Sylow | #6856 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #4175 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C23×C3 |
| Frattini | C33 | C22×C3×D3 |
| Fitting | C22×#6856 | C2 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
563 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 563 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1029);