Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of (((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×(((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| unambiguous semidirect product | (C2×((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| Fitting | C2×C32⋊H(3,𝔽3) ⋊ C22 |
| derived | C3×H(3,𝔽3) ⋊ C23×C3 |
| Sylow | C32⋊H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | C3×H(3,𝔽3) | C23×C3 |
| Frattini | C32 | C2×C3×D32 |
| Fitting | C2×C32⋊H(3,𝔽3) | C22 |
| socle | C2×C32 | C3×D32 |
| LCS | G ▷ C3×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
642 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
78 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2683);