Finite Group DatabasebetaFinite Group Databasebeta| order | 21507 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×C67⋊C3 |
| unambiguous semidirect product | C67⋊(C3×C107) |
| unambiguous semidirect product | (C67×C107)⋊C3 |
| Fitting, socle, Hall | C67×C107 ⋊ C3 |
| derived, Sylow | C67 ⋊ C3×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C3×C107 |
| Frattini | C1 | G |
| Fitting, socle | C67×C107 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C107 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7169 |
2675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21507, 1);