Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of (C22⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C22⋊C9)⋊C32 |
| derived | C22⋊C9 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | (C22⋊C9)⋊C2 |
| commutator, hypocenter | C22⋊C9 | C32 |
| Frattini | C3×C16 | S4 |
| Fitting | C22×C3×C16 | D3 |
| socle, prime radical | C23×C3 | C3⋊C16 |
| cosocle | C16×C22⋊C9 | C2 |
| LCS | G ▷ C22⋊C9 | |
| UCS | C1 ◁ C16 | |
68 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^5,3^2,2^2|a^2=b,b^2=c,c^2=d,d^2=e,f^3=g,f^a=f^2g^2,g^a=g^2,h^a=hi,h^f=i,i^f=hi144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153944);