Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
201 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 34 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^3=d,e^3=f,e^a=e^2f^2,f^a=f^2,g^a=gh,c^b=cd,e^b=ef,g^e=h,h^e=gh75 conjugacy classes — view the full character table.
| maximal subgroup of | #72220173, #72220195, C2×#14517984 |
| maximal normal subgroup of | #72220195, C2×#14517984 |
| maximal quotient of | #72220173, #72245167, C2×#14517984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2378);