Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #11757853⋊C2 |
| Fitting | C22×C3×3−1+2 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×(C3⋊S4)⋊C3 |
| commutator, cosocle, hypocenter | C22⋊H(3,𝔽3) | C2×C32 |
| Frattini | C32 | C32×S4 |
| Fitting | C22×C3×3−1+2 | D3 |
| socle | C22×C3 | C3×(C3⋊D3)⋊C3 |
| hypercenter | C9 | (C3⋊S4)⋊C3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C3 ◁ C9 | |
197 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^5,2^2|b^3=f^2,d^a=d^2,e^a=e^2f,g^a=gh,c^b=cf^2,d^c=de^2,e^d=ef,g^d=h,h^d=gh67 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2382);