Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23×C33 |
| direct product | C2×((C3⋊D3)⋊C3)⋊(C3⋊D3) |
| Fitting | C2×C32×H(3,𝔽3) ⋊ C22 |
| derived, Sylow | C32×H(3,𝔽3) ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | ((C3⋊D3)⋊C3)⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C32×H(3,𝔽3) | C23 |
| Frattini | C3 | C2×D3×C3⋊(C3⋊D3) |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | D32 |
| LCS | G ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2 | |
2180 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 2180 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3717);