Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C32 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D32 |
| commutator, hypocenter | C32 | C2×C64 |
| Fitting, cosocle | C32×C32 | C22 |
| socle | C2×C32 | C2×C32 |
| prime radical | C2×C3⋊D3 | C32 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C32 | |
97 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=c,c^2=d,d^2=e,e^2=f,f^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, 7102);