Finite Group DatabasebetaFinite Group Databasebeta| order | 21306 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D53×C67⋊C3 |
| unambiguous semidirect product | C53⋊(C2×C67⋊C3) |
| unambiguous semidirect product | (C67×D53)⋊C3 |
| Fitting, socle, derived, Hall | C53×C67 ⋊ C2×C3 |
| Hall | C53×C67⋊C3 ⋊ C2 |
| Hall | C67×D53 ⋊ C3 |
| Sylow | C67 ⋊ C3×D53 |
| Sylow | C53 ⋊ C2×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C53×C67 | C2×C3 |
| LCS | G ▷ C53×C67 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3551 |
700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21306, 11);