Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C32×#41 ⋊ C22 |
| Sylow | C32 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D32 |
| commutator, socle, cosocle | C2×C32 | C25 |
| Fitting | C32×#41 | C22 |
| hypercenter | #41 | D32 |
| hypocenter | C32 | #585 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ #41 | |
1703 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=f,e^2=f,e^a=ef,h^a=h^2,d^b=df,g^b=g^2,e^c=ef,e^d=ef81 conjugacy classes — view the full character table.
| maximal subgroup of | #11864965, #11864968, #11864971, … |
| maximal normal subgroup of | #11864965, #11864968, #11864971, … |
| maximal quotient of | #11900127, #11900134, #11900150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8579);