Finite Group DatabasebetaFinite Group Databasebeta| order | 29694 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D2121 |
| unambiguous semidirect product | C3⋊(C7×D707) |
| unambiguous semidirect product | C7⋊(C7×D303) |
| unambiguous semidirect product | C101⋊(C7×D21) |
| Fitting, socle, Hall | C3×C72×C101 ⋊ C2 |
| derived | C3×C7×C101 ⋊ C2×C7 |
| Hall | C72×C101 ⋊ D3 |
| Hall | C3×C101 ⋊ C7×D7 |
| Hall | C3×C72 ⋊ D101 |
| Sylow | C101 ⋊ C7×D21 |
| Sylow | C72 ⋊ D303 |
| Sylow | C3 ⋊ C7×D707 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D2121 |
| commutator, cosocle, hypocenter | C3×C7×C101 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C101 | C2 |
| LCS | G ▷ C3×C7×C101 | |
| UCS | C1 ◁ C7 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4242 |
7434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29694, 44);