Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | (C3×A4)⋊H(3,𝔽3) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | C3⋊(C3⋊S4) |
| commutator, cosocle, hypocenter | (C3×A4)⋊H(3,𝔽3) | C2 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3⋊(C3⋊D3) |
| LCS | G ▷ (C3×A4)⋊H(3,𝔽3) | |
| UCS | C1 ◁ C32 | |
642 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 50 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:
2,3^5,2^2|b^a=b^2,c^a=c^2,d^a=d^2,g^a=gh,d^b=df,g^b=h,h^b=gh,d^c=de69 conjugacy classes — view the full character table.
| maximal subgroup of | #72220513, #72220655, #72222951, … |
| maximal normal subgroup of | #72220655, #72222951, #72222953 |
| maximal quotient of | #72220513, #72259837, #72259892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2512);