Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32 |
No aliases for this group.
| derived, Sylow | C32×H(3,𝔽3) ⋊ C2×C4 |
1399 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 1399 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) = 72 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,g^a=g^2,d^b=d^2,e^b=e^2,f^b=f^2,f^e=fh126 conjugacy classes — view the full character table.
| maximal subgroup of | #72259624, #72259784, #72259785 |
| maximal normal subgroup of | #72259624, #72259784, #72259785 |
| maximal quotient of | #72229107 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 3176);