Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×#6157 |
| Fitting, Hall | C49×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C4×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | #6157 |
| commutator, hypocenter | C53 | C4×C49 |
| Frattini | C7 | C7×#6157 |
| Fitting | C49×C53 | C4 |
| socle | C7×C53 | C4×C7 |
| prime radical, cosocle | C7×D53 | C2×C7 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C49 | |
18 conjugacy classes of subgroups.
833 conjugacy classes — view the full character table.
| maximal subgroup of | C49⋊C3×#6157, C3×C49×#6157, C49×C3⋊#6157 |
| maximal normal subgroup of | C49⋊C3×#6157, C3×C49×#6157 |
| maximal quotient of | C3×C49×#6157, C49×C3⋊#6157 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 6);