Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C22×C3×C27 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C3⋊S4 |
| commutator, hypocenter | C22⋊H(3,𝔽3) | C2×C9 |
| Frattini | C9 | C3×C3⋊S4 |
| Fitting | C22×C3×C27 | D3 |
| socle | C22×C3 | C9×C3⋊D3 |
| prime radical | #6258 | C9 |
| cosocle | #66436 | C2×C3 |
| LCS | G ▷ C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C27 | |
151 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^5,2^2|b^3=c,c^3=f,d^a=d^2,e^a=e^2,g^a=gh,e^d=ef,g^d=h,h^d=gh171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2415);