Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×C3⋊D3 |
| commutator, socle | C2×C32 | C22×C8 |
| Fitting | C32×#131 | C2 |
| prime radical | C32×#41 | C4 |
| cosocle | C32×C8 | C23 |
| hypercenter | #131 | C3⋊D3 |
| hypocenter | C32 | #504 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ #131 | |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=d,d^2=e,e^2=f,g^a=g^2,h^a=h^2,c^b=cf120 conjugacy classes — view the full character table.
| maximal subgroup of | #11772720, #11797547, #11797556, … |
| maximal normal subgroup of | #11772720, #11797547, #11797556, … |
| maximal quotient of | #11795879, #11795999, #11797018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4721);