Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of C3⋊D3×((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×((C3⋊D3)⋊C3)⋊C2 |
| Fitting, derived, Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×H(3,𝔽3) | C23 |
| Frattini | C3 | D32×C3⋊D3 |
| socle | C33 | C2×D32 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 | |
1200 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
66 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3570);