Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #10619756⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619756⋊C3 |
| derived | #66361 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #66361 | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C3 | C3×#272 |
| LCS | G ▷ #66361 | |
| UCS | C1 | |
266 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2,3^5,2^2|c^3=f^2,c^a=c^2f,d^a=d^2,f^a=f^2,g^a=gh,d^b=df,d^c=de,e^c=ef,g^c=h,h^c=gh,e^d=ef^261 conjugacy classes — view the full character table.
| maximal subgroup of | #72259837, #72260026, #72260057, … |
| maximal normal subgroup of | #72276237 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2454);