Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D32 |
| commutator, socle, prime radical | C22×C32 | C22×C8 |
| Fitting | C32×C4×C8 | C22 |
| cosocle | C2×C32×C8 | C23 |
| hypercenter | C4×C8 | D32 |
| hypocenter | C32 | #2183 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
281 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,i^a=hi^2,h^c=h^2,i^c=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 32042);