Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | PSU(3,𝔽2) |
| commutator | C3⋊D3 | C2×C16 |
| Fitting | C32×C8 | Q8 |
| socle | C2×C32 | C4⋊C8 |
| prime radical | C2×C3⋊D3 | C2×C8 |
| cosocle | C8×C3⋊D3 | C22 |
| hypocenter | C32 | C4⋊C16 |
| LCS | G ▷ C3⋊D3 ▷ C32 | |
| UCS | C1 ◁ C8 | |
61 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=cde,d^2=e,e^2=f,b^a=bc,g^a=g^2h^2,h^a=g^2h,g^b=gh^2,h^b=g^2h^2,g^c=g^2,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | GO+(4,𝔽2)⋊C16, #11771562, #11772055, … |
| maximal normal subgroup of | GO+(4,𝔽2)⋊C16, #11771562, #11772055, … |
| maximal quotient of | #11772173, #11772216, #11772272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1964);