Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #10619744 |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C9) | C2×C3 |
| Frattini | C33 | C3×S4 |
| Fitting | C22×C32⋊C9 | D3 |
| socle | C22×C32 | (C3⋊D3)⋊C3 |
| prime radical | #10619761 | C3 |
| LCS | G ▷ C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C3 | |
109 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 109 conjugacy classes of subgroups — too many to draw. Only its 16 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2,3^5,2^2|b^3=e^2,c^3=f,c^a=c^2f^2,d^a=d^2e,f^a=f^2,g^a=gh,c^b=cd^2,d^b=df^2,d^c=de,g^c=h,h^c=gh61 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 814);