Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | D4×Q8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #3523 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C22×C9 | C25 |
| Frattini, socle | C22×C3 | C24×D3 |
| Fitting | D4×Q8×C9 | C2 |
| prime radical | #63501 | C22 |
| hypercenter | D4×Q8 | D9 |
| hypocenter | C9 | #3523 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1488 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=f,d^2=f,e^2=fg,h^3=i,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^e=h^2i^2,i^e=i^2144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 143853);