Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #396⋊C9 |
| derived | #95 ⋊ C2×C9 |
| Sylow | #396 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #126⋊C3 |
| commutator, hypocenter | #95 | C2×C9 |
| Frattini, socle | C23×C3 | C2×A4 |
| Fitting | C3×#396 | C3 |
| prime radical | C24×C3 | A4 |
| cosocle | C3×#95 | C2×C3 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C3 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2,3^2,2^5|b^3=c,d^2=fg,e^2=fh,d^a=df,e^a=egh,d^b=e,e^b=deg,f^b=gh,g^b=fg,e^d=eh54 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#396⋊C9, #2401⋊C9, #2643⋊C9, … |
| maximal normal subgroup of | C2×#396⋊C9, #2401⋊C9, #2643⋊C9, … |
| maximal quotient of | #1443⋊C9, #2069⋊C9, #2070⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 200);