Finite Group DatabasebetaFinite Group Databasebeta| order | 35700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#14523665 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #14523665 |
| commutator, cosocle, hypocenter | C3×C52×C7 | C22×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C17 | C22 |
| LCS | G ▷ C3×C52×C7 | |
| UCS | C1 ◁ C17 | |
192 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3570 |
2652 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35700, 462);