Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| derived, Sylow | C42×Q8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C22⋊(C42⋊C3) |
| commutator, hypocenter | C42×Q8 | C9 |
| Frattini, socle, prime radical | C23×C3 | C22⋊A4 |
| Fitting, cosocle | C3×C42×Q8 | C3 |
| LCS | G ▷ C42×Q8 | |
| UCS | C1 ◁ C2×C3 | |
263 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
3^2,2^7|a^3=b,c^2=h,d^2=i,e^2=gi,f^2=gh,c^a=dgh,d^a=cdg,e^a=ef,f^a=egh,h^a=i,i^a=ghi,d^c=dg96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153650);