Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C9×M32 ⋊ C2 |
| Sylow | C9 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×D9 |
| commutator | C2×C9 | C22×C8 |
| Frattini | C3×C8 | C22×D3 |
| Fitting | C9×M32 | C2 |
| socle | C2×C3 | C2×D3×C8 |
| prime radical | #3697 | C4 |
| cosocle | C8×C9 | C23 |
| hypercenter | M32 | D9 |
| hypocenter | C9 | #504 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C8 ◁ M32 | |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|c^2=d,d^2=e,e^2=f,g^3=h^2,b^a=bf,g^a=g^2h,h^a=h^2,c^b=cf120 conjugacy classes — view the full character table.
| maximal subgroup of | #11797546, #11797552, #11797582, … |
| maximal normal subgroup of | #11797546, #11797552, #11797582, … |
| maximal quotient of | #11795881, #11795884, #11795992, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 469);