Finite Group DatabasebetaFinite Group Databasebeta| order | 35700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C5 |
| direct product | C3×C7×#13133347 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | #13133347 |
| commutator, hypocenter | C52×C17 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C17 | C4 |
| prime radical | C3×C7×C5⋊D85 | C2 |
| cosocle | C5⋊D85 | C2×C3×C7 |
| LCS | G ▷ C52×C17 | |
| UCS | C1 ◁ C3×C7 | |
128 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3570 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35700, 390);