Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #6867 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92175⋊C2 |
| commutator, Fitting, cosocle | C2×#6867 | C22 |
| Frattini, prime radical | C2×C33 | D32 |
| socle | C2×C32 | ((C3⋊D3)⋊C3)⋊C2 |
| hypocenter | #6867 | Q8 |
| LCS | G ▷ C2×#6867 ▷ #6867 | |
| UCS | C1 ◁ C2 | |
126 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^3,3^5|a^2=c,b^2=c,d^3=h^2,e^3=f,b^a=bc,e^a=e^2f^2,f^a=f^2,g^a=g^2h,d^b=d^2h,g^b=g^2,h^b=h^2,e^d=eg,g^e=gh57 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 177);