Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #11919920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C82⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C82⋊C9 | C2 |
| Frattini | C3×C42 | S4 |
| Fitting | C3×C82 | D3 |
| socle | C22×C3 | #857 |
| LCS | G ▷ C82⋊C9 | |
| UCS | C1 | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2,3^2,2^6|b^3=c,d^2=f,e^2=g,f^2=h,g^2=i,b^a=b^2c^2,c^a=c^2,d^a=deh,e^a=eg,f^a=fg,g^a=gi,h^a=hi,d^b=efgi,e^b=defhi,f^b=ghi,g^b=fgh,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, 153931);