Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×C3⋊((C3⋊D3)⋊C3) |
| commutator, cosocle | C2×C34 | C22×C3 |
| Frattini | C2×C3 | C3×D3×C3⋊D3 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3×D3 |
| hypocenter | C34 | C3×D4 |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 | |
919 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 919 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^a=bd,g^a=g^2,e^b=e^2,f^b=f^2,h^b=h^2,f^c=fh117 conjugacy classes — view the full character table.
| maximal subgroup of | #72229139, (C3⋊D3)⋊C3×#626, #72259996, … |
| maximal normal subgroup of | (C3⋊D3)⋊C3×#626, #72259996, #72260006, … |
| maximal quotient of | #72229139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3070);