Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Sylow | C32×H(3,𝔽3) ⋊ D4 |
1460 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1460 conjugacy classes of subgroups — too many to draw. Only its 156 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|a^2=c,b^a=bc,g^a=g^2,h^a=h^2,d^b=d^2,e^b=e^2,f^b=f^2,h^b=h^2,g^f=gh99 conjugacy classes — view the full character table.
| maximal subgroup of | #72229139, #72259876, #72259972 |
| maximal normal subgroup of | #72229139, #72259876, #72259972 |
| maximal quotient of | #72229131 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3172);