Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting | C22×C3×H(3,𝔽3) ⋊ D3 |
| derived | C3×C22⋊H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | A4⋊((C3⋊D3)⋊C3) |
| commutator, cosocle, hypocenter | C3×C22⋊H(3,𝔽3) | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C3×H(3,𝔽3) | D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C3×C22⋊H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
462 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 33 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3^5,2^2|c^a=c^2,d^a=d^2,e^a=e^2,g^a=gh,d^b=de,d^c=df,g^c=h,h^c=gh69 conjugacy classes — view the full character table.
| maximal subgroup of | #72220531, #72222924, #72222953, … |
| maximal normal subgroup of | #72222924, #72222953, #72222974 |
| maximal quotient of | #72220531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2460);