Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | (C22⋊C9)⋊C2 |
| commutator, hypocenter | Q8⋊C9 | C16 |
| Frattini | C3×C16 | S4 |
| Fitting | C3×#504 | D3 |
| socle | C2×C3 | A4⋊C16 |
| prime radical | C3×#41 | C3⋊C8 |
| cosocle | #504⋊C9 | C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C16 | |
61 conjugacy classes of subgroups.
| minimal degree | μ(G) = 137 |
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^4,3^2,2^3|a^2=b,b^2=c,c^2=d,d^2=i,e^3=f,g^2=i,h^2=i,e^a=e^2f^2,f^a=f^2,g^a=gh,h^a=hi,g^e=h,h^e=ghi,h^g=hi120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153945);