Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C32×SD16 ⋊ C22 |
| Sylow | C32 ⋊ #577 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D4 |
| commutator, cosocle | C32×C4 | C24 |
| Frattini | C4 | C22×D32 |
| Fitting | C32×SD16 | C22 |
| socle | C2×C32 | C22×D4 |
| hypercenter | SD16 | D32 |
| hypocenter | C32 | #577 |
| LCS | G ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|c^2=f,e^2=f,b^a=bf,h^a=h^2,d^b=df,g^b=g^2,d^c=de,e^c=ef,e^d=ef54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5762, #11918857, D3×#5778, … |
| maximal normal subgroup of | D3×#5762, #11918857, D3×#5778, … |
| maximal quotient of | #11858015, #11858072, #11858560, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6633);