Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C32 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D32 |
| commutator, hypocenter | C32 | C2×C32 |
| Fitting, cosocle | C32×C16 | C22 |
| socle | C2×C32 | C2×C16 |
| prime radical | C2×C3⋊D3 | C16 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C16 | |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=c,c^2=d,d^2=e,e^2=f,h^a=h^2,g^b=g^2144 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊C32, #11772727, #11772921, … |
| maximal normal subgroup of | D32⋊C32, #11772727, #11772921, … |
| maximal quotient of | #11772653, #11772694, #11773014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 949);