Finite Group DatabasebetaFinite Group Databasebeta| order | 35322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C29 |
| direct product | C7×(C29⋊D29)⋊C3 |
| Fitting, socle, Hall | C7×C292 ⋊ C2×C3 |
| derived, Sylow | C292 ⋊ C2×C3×C7 |
| Hall | C7×C292⋊C3 ⋊ C2 |
| Hall | C7×C29⋊D29 ⋊ C3 |
| Hall | C292⋊C3 ⋊ C2×C7 |
| Hall | C29⋊D29 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | (C29⋊D29)⋊C3 |
| commutator, cosocle, hypocenter | C292 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C292 | C2×C3 |
| LCS | G ▷ C292 | |
| UCS | C1 ◁ C7 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 609 |
1022 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35322, 60);