Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived | C22⋊#6855 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C9⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C22⋊#6855 | C2 |
| Frattini | C33 | C3⋊S4 |
| Fitting | C22×C32×C9 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C22⋊#6855 | |
| UCS | C1 ◁ C3 | |
279 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3^5,2^2|b^3=f,c^3=e,b^a=b^2f^2,c^a=c^2e^2,e^a=e^2,f^a=f^2,g^a=gh,c^b=cd,g^b=h,h^b=gh99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 883);