Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting | C22×C32⋊H(3,𝔽3) ⋊ C2 |
| Sylow | C32⋊H(3,𝔽3) ⋊ D4 |
1105 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1105 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^3,3^5|b^a=bc,d^a=d^2,e^a=e^2,f^a=f^2,f^d=fh,f^e=fg129 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#92338, #72229235, #72259905, … |
| maximal normal subgroup of | D4×#92338, #72229235, #72259905, … |
| maximal quotient of | #72228545 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2150);