Finite Group DatabasebetaFinite Group Databasebeta| order | 29547 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×C67⋊C9 |
| unambiguous semidirect product | C67⋊(C72×C9) |
| derived, Sylow | C67 ⋊ C72×C9 |
| Hall | C72×C67 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C67⋊C3 |
| commutator, hypocenter | C67 | C72×C9 |
| Frattini | C3 | C72×C67⋊C3 |
| Fitting, socle, prime radical | C3×C72×C67 | C3 |
| cosocle | C3×C67 | C3×C72 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C72 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 29547 |
3675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29547, 21);