Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | C22⋊(C22⋊(C22⋊C9)) |
| derived, Sylow | C26 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊(C22⋊A4) |
| commutator, hypocenter | C26 | C9 |
| Fitting, socle, prime radical, cosocle | C26×C3 | C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C3 | |
1986 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
3^2,2^6|a^3=b,c^a=cd,d^a=c,e^a=ef,f^a=e,g^a=gh,h^a=g72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8266);