Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
No aliases for this group.
| derived, Sylow | C32 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4×C8 | D32 |
| commutator, hypocenter | C32 | C8×C16 |
| Fitting, cosocle | C32×C4×C8 | C22 |
| socle, prime radical | C22×C32 | C4×C8 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
245 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^7,3^2|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,i^a=hi^2,h^b=h^2,i^b=i^2288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5301);