Finite Group DatabasebetaFinite Group Databasebeta| order | 10353 |
| isoclinism | isoclinic class of C29⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C3×C17×C29 ⋊ C7 |
| derived, Sylow | C29 ⋊ C3×C7×C17 |
| Hall | C17×C29 ⋊ C3×C7 |
| Hall | C3×C29 ⋊ C7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | C29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C3×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C29 | C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C3×C17 | |
16 conjugacy classes of subgroups.
561 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10353, 2);