Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3×C4 |
No aliases for this group.
| Sylow | C32 ⋊ #384 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C3⋊D3 |
| commutator | C22×C32 | C22×C4 |
| Fitting | C2×C32×C42 | C2 |
| socle, prime radical, cosocle | C23×C32 | C23 |
| hypercenter | C2×C42 | C3⋊D3 |
| hypocenter | C32 | #384 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
558 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=f,c^2=e,b^a=bf,c^a=ce,g^a=g^2,h^a=h^2156 conjugacy classes — view the full character table.
| maximal subgroup of | #11771079, #11771083, #11771477, … |
| maximal normal subgroup of | #11771079, #11771083, #11771477, … |
| maximal quotient of | #11773204, #11773439, #11786178, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4516);