Finite Group DatabasebetaFinite Group Databasebeta| order | 6572 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#6157 |
| Fitting, socle, Hall | C31×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #6157 |
| commutator, hypocenter | C53 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C53 | C4 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
527 conjugacy classes — view the full character table.
| maximal subgroup of | C31⋊C3×#6157, C3×C31×#6157, C31×C3⋊#6157, … |
| maximal normal subgroup of | C31⋊C3×#6157, C3×C31×#6157, ΓL(1,𝔽32)×#6157, … |
| maximal quotient of | C3×C31×#6157, C31×C3⋊#6157, C5×C31×#6157, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6572, 6);