Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| Fitting, derived | C22×C3×H(3,𝔽3) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊((C3⋊D3)⋊A4) |
| commutator, Fitting, cosocle, hypocenter | C22×C3×H(3,𝔽3) | C2×C3 |
| Frattini | C32 | A4×C3⋊D3 |
| socle | C22×C32 | C3×C3⋊D3 |
| LCS | G ▷ C22×C3×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
573 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 36 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:
2,3,2^2,3^4|e^a=e^2,f^a=f^2,g^a=g^2,c^b=cd,d^b=c,f^b=fg,f^e=fh60 conjugacy classes — view the full character table.
| maximal subgroup of | #72220531, #72222931, #72222951, … |
| maximal normal subgroup of | #72222931, #72222951, #72222974, … |
| maximal quotient of | #72220531, #72276187 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2653);