Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊(#1454⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | C3⋊(#1454⋊C3) |
| unambiguous semidirect product | #68049⋊C3 |
| Fitting, derived | C3×C82 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C82 | C2×C3 |
| Frattini | C42 | D3×A4 |
| socle | C22×C3 | C2×C42⋊C3 |
| LCS | G ▷ C3×C82 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3,2^2,3,2^4|c^2=g,d^2=fg,f^2=i,g^2=hi,c^a=ci,d^a=dhi,e^a=e^2,c^b=di,d^b=cdf,f^b=gi,g^b=fg,h^b=i,i^b=hi48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154155);