Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(#6869⋊C2) |
| Fitting | C4×#6869 ⋊ C2 |
| Sylow | #6869 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×#6869⋊C2 |
| commutator, cosocle | C2×#6869 | C22 |
| Frattini | C2×C3×C9 | C2×C3⋊D3 |
| Fitting | C4×#6869 | C2 |
| socle | C2×C3 | C2×#4181 |
| hypercenter | C4 | #6869⋊C2 |
| hypocenter | #6869 | D4 |
| LCS | G ▷ C2×#6869 ▷ #6869 | |
| UCS | C1 ◁ C2 ◁ C4 | |
222 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 42 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^2=c,e^3=g,g^3=h^2,b^a=bc,d^a=d^2,e^a=e^2g^2h,f^a=fh^2,g^a=g^2h,h^a=h^2,e^d=ef,f^e=fh111 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 527);