Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | #2811 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #5450 |
| commutator, hypocenter | C22×Q8 | C22×C9 |
| Frattini, socle, prime radical | C23×C3 | C22×A4 |
| Fitting | C3×#2811 | C3 |
| cosocle | C22×C3×Q8 | C22×C3 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2×C3 | |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3^2,2^5|a^2=i,b^2=i,c^3=d,e^2=i,f^2=i,b^a=bi,e^a=eg,f^a=fh,e^b=egh,f^b=fg,e^c=f,f^c=efi,g^c=h,h^c=gh,f^e=fi72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153488);