Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C8×C9 ⋊ C2 |
| Sylow | C9 ⋊ #493 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D36 |
| commutator, cosocle | C2×C4×C9 | C23 |
| Frattini | C2×C3×C4 | C22×D3 |
| Fitting | C4×C8×C9 | C2 |
| socle | C22×C3 | C2×D12 |
| hypercenter | C4×C8 | D9 |
| hypocenter | C9 | #493 |
| LCS | G ▷ C2×C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ C4×C8 | |
243 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=df,d^2=f,g^3=h^2,b^a=be,c^a=cd,d^a=df,g^a=g^2h,h^a=h^2150 conjugacy classes — view the full character table.
| maximal subgroup of | #11772005, #11772057, #11772063, … |
| maximal normal subgroup of | #11772005, #11772057, #11772063, … |
| maximal quotient of | #11782440, #11782532, #11782587, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 259);