Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C8 | D32 |
| commutator | C2×C32 | C4×C8 |
| Fitting, cosocle | C2×C32×C8 | C22 |
| socle, prime radical | C22×C32 | C2×C8 |
| hypocenter | C32 | #346 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2×C8 | |
122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bf,h^a=h^2,g^b=g^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4502, #11795835, D3×#4461, … |
| maximal normal subgroup of | D3×#4502, #11795835, D3×#4461, … |
| maximal quotient of | #11771301, #11771315, #11772266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 985);